diff --git a/pygmt/clib/session.py b/pygmt/clib/session.py
index 95ed8c19d76..97d25ad1c55 100644
--- a/pygmt/clib/session.py
+++ b/pygmt/clib/session.py
@@ -17,7 +17,6 @@
 import numpy as np
 import pandas as pd
 import xarray as xr
-from packaging.version import Version
 from pygmt.clib.conversion import (
     array_to_datetime,
     as_c_contiguous,
@@ -199,15 +198,8 @@ def info(self):
                 "cores": self.get_default("API_CORES"),
                 "grid layout": self.get_default("API_GRID_LAYOUT"),
             }
-            # For GMT<6.4.0, API_IMAGE_LAYOUT is not defined if GMT is not
-            # compiled with GDAL. Since GMT 6.4.0, GDAL is a required GMT
-            # dependency. The code block can be refactored after we bump
-            # the minimum required GMT version to 6.4.0.
-            with contextlib.suppress(GMTCLibError):
-                self._info["image layout"] = self.get_default("API_IMAGE_LAYOUT")
-            # API_BIN_VERSION is new in GMT 6.4.0.
-            if Version(self._info["version"]) >= Version("6.4.0"):
-                self._info["binary version"] = self.get_default("API_BIN_VERSION")
+            self._info["image layout"] = self.get_default("API_IMAGE_LAYOUT")
+            self._info["binary version"] = self.get_default("API_BIN_VERSION")
         return self._info
 
     def __enter__(self):
diff --git a/pygmt/src/timestamp.py b/pygmt/src/timestamp.py
index 39a6c25bf39..d09a86f446d 100644
--- a/pygmt/src/timestamp.py
+++ b/pygmt/src/timestamp.py
@@ -53,7 +53,7 @@ def timestamp(
     font
         Font of the timestamp and the optional label. Since the GMT logo has a fixed
         height, the font sizes are fixed to be 8-point for the timestamp and 7-point for
-        the label. The parameter can't change the font color for GMT<=6.4.0, only the
+        the label. The parameter can't change the font color for GMT 6.4.0, only the
         font style.
     timefmt
         Format string for the UNIX timestamp. The format string is parsed by the C
@@ -83,8 +83,8 @@ def timestamp(
         kwdict["U"] += f"{label}"
     kwdict["U"] += f"+j{justify}"
 
-    if Version(__gmt_version__) <= Version("6.4.0") and "/" not in str(offset):
-        # Giving a single offset doesn't work in GMT <= 6.4.0.
+    if Version(__gmt_version__) < Version("6.5.0") and "/" not in str(offset):
+        # Giving a single offset doesn't work in GMT < 6.5.0.
         # See https://github.com/GenericMappingTools/gmt/issues/7107.
         offset = f"{offset}/{offset}"
     kwdict["U"] += f"+o{offset}"
@@ -98,8 +98,8 @@ def timestamp(
                 "The given text string will be truncated to 64 characters."
             )
             warnings.warn(message=msg, category=RuntimeWarning, stacklevel=2)
-        if Version(__gmt_version__) <= Version("6.4.0"):
-            # workaround for GMT<=6.4.0 by overriding the 'timefmt' parameter
+        if Version(__gmt_version__) < Version("6.5.0"):
+            # Workaround for GMT<6.5.0 by overriding the 'timefmt' parameter
             timefmt = text[:64]
         else:
             kwdict["U"] += f"+t{text}"
diff --git a/pygmt/tests/test_accessor.py b/pygmt/tests/test_accessor.py
index e5e4534e1c3..2701d2a0b3a 100644
--- a/pygmt/tests/test_accessor.py
+++ b/pygmt/tests/test_accessor.py
@@ -73,10 +73,6 @@ def test_accessor_set_non_boolean():
         grid.gmt.gtype = 2
 
 
-@pytest.mark.skipif(
-    Version(__gmt_version__) < Version("6.4.0"),
-    reason="Upstream bug fixed in https://github.com/GenericMappingTools/gmt/pull/6615",
-)
 @pytest.mark.xfail(
     condition=sys.platform == "win32" and Version(__gmt_version__) < Version("6.5.0"),
     reason="Upstream bug fixed in https://github.com/GenericMappingTools/gmt/pull/7573",
diff --git a/pygmt/tests/test_clib.py b/pygmt/tests/test_clib.py
index 7591aff0729..7747c1551bc 100644
--- a/pygmt/tests/test_clib.py
+++ b/pygmt/tests/test_clib.py
@@ -11,6 +11,7 @@
 import xarray as xr
 from packaging.version import Version
 from pygmt import Figure, clib
+from pygmt.clib import required_gmt_version
 from pygmt.clib.conversion import dataarray_to_matrix
 from pygmt.clib.session import FAMILIES, VIAS
 from pygmt.exceptions import (
@@ -531,7 +532,7 @@ def test_get_default():
     with clib.Session() as lib:
         assert lib.get_default("API_GRID_LAYOUT") in {"rows", "columns"}
         assert int(lib.get_default("API_CORES")) >= 1
-        assert Version(lib.get_default("API_VERSION")) >= Version("6.3.0")
+        assert Version(lib.get_default("API_VERSION")) >= Version(required_gmt_version)
         assert lib.get_default("PROJ_LENGTH_UNIT") == "cm"
 
 
diff --git a/pygmt/tests/test_datasets_load_remote_datasets.py b/pygmt/tests/test_datasets_load_remote_datasets.py
index b46e21e2f94..b2de1ebddfa 100644
--- a/pygmt/tests/test_datasets_load_remote_datasets.py
+++ b/pygmt/tests/test_datasets_load_remote_datasets.py
@@ -32,10 +32,8 @@ def test_load_remote_dataset_benchmark_with_region():
     assert data.attrs["horizontal_datum"] == "WGS84"
     assert data.gmt.registration == 0
     assert data.shape == (11, 21)
-    # The cpt attribute was added since GMT 6.4.0
     # Can't access the cpt attribute using virtual files
-    # if Version(__gmt_version__) >= Version("6.4.0"):
-    #    assert data.attrs["cpt"] == "@earth_age.cpt"
+    # assert data.attrs["cpt"] == "@earth_age.cpt"
 
 
 def test_load_remote_dataset_invalid_resolutions():
diff --git a/pygmt/tests/test_grdfill.py b/pygmt/tests/test_grdfill.py
index 35be47ebef4..f7c4730b744 100644
--- a/pygmt/tests/test_grdfill.py
+++ b/pygmt/tests/test_grdfill.py
@@ -7,9 +7,7 @@
 import numpy as np
 import pytest
 import xarray as xr
-from packaging.version import Version
 from pygmt import grdfill, load_dataarray
-from pygmt.clib import __gmt_version__
 from pygmt.exceptions import GMTInvalidInput
 from pygmt.helpers import GMTTempFile
 from pygmt.helpers.testing import load_static_earth_relief
@@ -86,16 +84,11 @@ def test_grdfill_dataarray_out(grid, expected_grid):
     xr.testing.assert_allclose(a=result, b=expected_grid)
 
 
-@pytest.mark.skipif(
-    Version(__gmt_version__) < Version("6.4.0"),
-    reason="Upstream bug/crash fixed in https://github.com/GenericMappingTools/gmt/pull/6418.",
-)
 def test_grdfill_asymmetric_pad(grid, expected_grid):
     """
     Test grdfill using a region that includes the edge of the grid.
 
-    Regression test for
-    https://github.com/GenericMappingTools/pygmt/issues/1745.
+    Regression test for https://github.com/GenericMappingTools/pygmt/issues/1745.
     """
     result = grdfill(grid=grid, mode="c20", region=[-55, -50, -24, -16])
     # check information of the output grid
diff --git a/pygmt/tests/test_grdfilter.py b/pygmt/tests/test_grdfilter.py
index a2604d8b00e..5cbe3574767 100644
--- a/pygmt/tests/test_grdfilter.py
+++ b/pygmt/tests/test_grdfilter.py
@@ -7,16 +7,11 @@
 import numpy as np
 import pytest
 import xarray as xr
-from packaging.version import Version
 from pygmt import grdfilter, load_dataarray
-from pygmt.clib import __gmt_version__
 from pygmt.exceptions import GMTInvalidInput
 from pygmt.helpers import GMTTempFile
 from pygmt.helpers.testing import load_static_earth_relief
 
-# GMT 6.3 on conda-forge doesn't have OpenMP enabled.
-cores = 2 if Version(__gmt_version__) > Version("6.3.0") else None
-
 
 @pytest.fixture(scope="module", name="grid")
 def fixture_grid():
@@ -51,7 +46,7 @@ def test_grdfilter_dataarray_in_dataarray_out(grid, expected_grid):
     Test grdfilter with an input DataArray, and output as DataArray.
     """
     result = grdfilter(
-        grid=grid, filter="g600", distance="4", region=[-53, -49, -20, -17], cores=cores
+        grid=grid, filter="g600", distance="4", region=[-53, -49, -20, -17], cores=2
     )
     # check information of the output grid
     assert isinstance(result, xr.DataArray)
diff --git a/pygmt/tests/test_grdlandmask.py b/pygmt/tests/test_grdlandmask.py
index d275da5cd4b..ae51ba2eda4 100644
--- a/pygmt/tests/test_grdlandmask.py
+++ b/pygmt/tests/test_grdlandmask.py
@@ -6,15 +6,10 @@
 
 import pytest
 import xarray as xr
-from packaging.version import Version
 from pygmt import grdlandmask, load_dataarray
-from pygmt.clib import __gmt_version__
 from pygmt.exceptions import GMTInvalidInput
 from pygmt.helpers import GMTTempFile
 
-# GMT 6.3 on conda-forge doesn't have OpenMP enabled.
-cores = 2 if Version(__gmt_version__) > Version("6.3.0") else None
-
 
 @pytest.fixture(scope="module", name="expected_grid")
 def fixture_expected_grid():
@@ -55,7 +50,7 @@ def test_grdlandmask_no_outgrid(expected_grid):
     """
     Test grdlandmask with no set outgrid.
     """
-    result = grdlandmask(spacing=1, region=[125, 130, 30, 35], cores=cores)
+    result = grdlandmask(spacing=1, region=[125, 130, 30, 35], cores=2)
     # check information of the output grid
     assert isinstance(result, xr.DataArray)
     assert result.gmt.gtype == 1  # Geographic grid
diff --git a/pygmt/tests/test_grdsample.py b/pygmt/tests/test_grdsample.py
index 11812a1226a..4c9e64139c3 100644
--- a/pygmt/tests/test_grdsample.py
+++ b/pygmt/tests/test_grdsample.py
@@ -6,15 +6,10 @@
 
 import pytest
 import xarray as xr
-from packaging.version import Version
 from pygmt import grdsample, load_dataarray
-from pygmt.clib import __gmt_version__
 from pygmt.helpers import GMTTempFile
 from pygmt.helpers.testing import load_static_earth_relief
 
-# GMT 6.3 on conda-forge doesn't have OpenMP enabled.
-cores = 2 if Version(__gmt_version__) > Version("6.3.0") else None
-
 
 @pytest.fixture(scope="module", name="grid")
 def fixture_grid():
@@ -80,7 +75,7 @@ def test_grdsample_dataarray_out(grid, expected_grid, region, spacing):
     """
     Test grdsample with no outgrid set and the spacing is changed.
     """
-    result = grdsample(grid=grid, spacing=spacing, region=region, cores=cores)
+    result = grdsample(grid=grid, spacing=spacing, region=region, cores=2)
     # check information of the output grid
     assert isinstance(result, xr.DataArray)
     assert result.gmt.gtype == 1  # Geographic grid
diff --git a/pygmt/tests/test_sph2grd.py b/pygmt/tests/test_sph2grd.py
index 820b8923240..89b4abeff25 100644
--- a/pygmt/tests/test_sph2grd.py
+++ b/pygmt/tests/test_sph2grd.py
@@ -6,14 +6,9 @@
 
 import numpy.testing as npt
 import pytest
-from packaging.version import Version
 from pygmt import sph2grd
-from pygmt.clib import __gmt_version__
 from pygmt.helpers import GMTTempFile
 
-# GMT 6.3 on conda-forge doesn't have OpenMP enabled.
-cores = 2 if Version(__gmt_version__) > Version("6.3.0") else None
-
 
 def test_sph2grd_outgrid():
     """
@@ -32,7 +27,7 @@ def test_sph2grd_no_outgrid():
     """
     Test sph2grd with no set outgrid.
     """
-    temp_grid = sph2grd(data="@EGM96_to_36.txt", spacing=1, region="g", cores=cores)
+    temp_grid = sph2grd(data="@EGM96_to_36.txt", spacing=1, region="g", cores=2)
     assert temp_grid.dims == ("y", "x")
     assert temp_grid.gmt.gtype == 0  # Cartesian grid
     assert temp_grid.gmt.registration == 0  # Gridline registration