diff --git a/ci/deps/actions-311-minimum_versions.yaml b/ci/deps/actions-311-minimum_versions.yaml
index f9dc5d2367344..a101498415ef8 100644
--- a/ci/deps/actions-311-minimum_versions.yaml
+++ b/ci/deps/actions-311-minimum_versions.yaml
@@ -8,9 +8,9 @@ dependencies:
 
   # build dependencies
   - versioneer
-  - cython<4.0.0a0
-  - meson=1.2.1
-  - meson-python=0.13.1
+  - cython>=3.1,<4.0.0a0
+  - meson>=1.6,<2
+  - meson-python>=0.17.1,<1
 
   # test dependencies
   - pytest>=7.3.2
diff --git a/ci/deps/actions-311.yaml b/ci/deps/actions-311.yaml
index deb646a7ba86a..51ac47a5e3bfe 100644
--- a/ci/deps/actions-311.yaml
+++ b/ci/deps/actions-311.yaml
@@ -6,9 +6,9 @@ dependencies:
 
   # build dependencies
   - versioneer
-  - cython<4.0.0a0
-  - meson=1.2.1
-  - meson-python=0.13.1
+  - cython>=3.1,<4.0.0a0
+  - meson>=1.6,<2
+  - meson-python>=0.17.1,<1
 
   # test dependencies
   - pytest>=7.3.2
diff --git a/ci/deps/actions-312.yaml b/ci/deps/actions-312.yaml
index 5a24b0c1077d0..3a79c37e880ba 100644
--- a/ci/deps/actions-312.yaml
+++ b/ci/deps/actions-312.yaml
@@ -6,9 +6,9 @@ dependencies:
 
   # build dependencies
   - versioneer
-  - cython<4.0.0a0
-  - meson=1.2.1
-  - meson-python=0.13.1
+  - cython>=3.1,<4.0.0a0
+  - meson>=1.6,<2
+  - meson-python>=0.17.1,<1
 
   # test dependencies
   - pytest>=7.3.2
diff --git a/ci/deps/actions-313-downstream_compat.yaml b/ci/deps/actions-313-downstream_compat.yaml
index c118bbcdf1697..13f46b9461983 100644
--- a/ci/deps/actions-313-downstream_compat.yaml
+++ b/ci/deps/actions-313-downstream_compat.yaml
@@ -7,9 +7,9 @@ dependencies:
 
   # build dependencies
   - versioneer
-  - cython<4.0.0a0
-  - meson=1.2.1
-  - meson-python=0.13.1
+  - cython>=3.1,<4.0.0a0
+  - meson>=1.6,<2
+  - meson-python>=0.17.1,<1
 
   # test dependencies
   - pytest>=7.3.2
diff --git a/ci/deps/actions-313-freethreading.yaml b/ci/deps/actions-313-freethreading.yaml
index e118080bc4c40..4639135ef284e 100644
--- a/ci/deps/actions-313-freethreading.yaml
+++ b/ci/deps/actions-313-freethreading.yaml
@@ -7,7 +7,7 @@ dependencies:
   # build dependencies
   - setuptools
   - versioneer
-  - cython<4.0.0a0
+  - cython>=3.1,<4.0.0a0
   - meson=1.8.0
   - meson-python=0.18.0
 
diff --git a/ci/deps/actions-313-numpydev.yaml b/ci/deps/actions-313-numpydev.yaml
index a1474d70c9487..b5b100737aca7 100644
--- a/ci/deps/actions-313-numpydev.yaml
+++ b/ci/deps/actions-313-numpydev.yaml
@@ -6,9 +6,9 @@ dependencies:
 
   # build dependencies
   - versioneer
-  - meson=1.2.1
-  - meson-python=0.13.1
-  - cython<4.0.0a0
+  - meson>=1.6,<2
+  - meson-python>=0.17.1,<1
+  - cython>=3.1,<4.0.0a0
 
   # test dependencies
   - pytest>=7.3.2
diff --git a/ci/deps/actions-313-pyarrownightly.yaml b/ci/deps/actions-313-pyarrownightly.yaml
index e56813cffb901..22310ac9a67d8 100644
--- a/ci/deps/actions-313-pyarrownightly.yaml
+++ b/ci/deps/actions-313-pyarrownightly.yaml
@@ -6,9 +6,9 @@ dependencies:
 
   # build dependencies
   - versioneer
-  - meson=1.2.1
-  - cython<4.0.0a0
-  - meson-python=0.13.1
+  - meson>=1.6,<2
+  - cython>=3.1,<4.0.0a0
+  - meson-python>=0.17.1,<1
 
   # test dependencies
   - pytest>=7.3.2
diff --git a/ci/deps/actions-313.yaml b/ci/deps/actions-313.yaml
index ffca09b901852..ed043ca08ec94 100644
--- a/ci/deps/actions-313.yaml
+++ b/ci/deps/actions-313.yaml
@@ -6,9 +6,9 @@ dependencies:
 
   # build dependencies
   - versioneer
-  - cython<4.0.0a0
-  - meson=1.2.1
-  - meson-python=0.13.1
+  - cython>=3.1,<4.0.0a0
+  - meson>=1.6,<2
+  - meson-python>=0.17.1,<1
 
   # test dependencies
   - pytest>=7.3.2
diff --git a/environment.yml b/environment.yml
index 1c7ebd0cea1ff..c2d9219c64189 100644
--- a/environment.yml
+++ b/environment.yml
@@ -8,9 +8,9 @@ dependencies:
 
   # build dependencies
   - versioneer
-  - cython<4.0.0a0
-  - meson=1.2.1
-  - meson-python=0.13.1
+  - cython>=3.1,<4.0.0a0
+  - meson>=1.6,<2
+  - meson-python>=0.17.1,<1
 
   # test dependencies
   - pytest>=7.3.2
diff --git a/pyproject.toml b/pyproject.toml
index 0ea46b92e9e01..73390924468ae 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -2,10 +2,10 @@
 # Minimum requirements for the build system to execute.
 # See https://github.com/scipy/scipy/pull/12940 for the AIX issue.
 requires = [
-    "meson-python>=0.13.1",
-    "meson>=1.2.1,<2",
+    "meson-python>=0.17.1,<1",
+    "meson>=1.6,<2",
     "wheel",
-    "Cython<4.0.0a0",  # Note: sync with setup.py, environment.yml and asv.conf.json
+    "Cython>=3.1,<4.0.0a0",  # Note: sync with setup.py, environment.yml and asv.conf.json
     # Force numpy higher than 2.0rc1, so that built wheels are compatible
     # with both numpy 1 and 2
     "numpy>=2.0.0rc1",
diff --git a/requirements-dev.txt b/requirements-dev.txt
index 708aa7567a009..106d395e3d065 100644
--- a/requirements-dev.txt
+++ b/requirements-dev.txt
@@ -3,9 +3,9 @@
 
 pip
 versioneer[toml]
-cython<4.0.0a0
-meson[ninja]==1.2.1
-meson-python==0.13.1
+cython>=3.1,<4.0.0a0
+meson[ninja]>=1.6,<2
+meson-python>=0.17.1,<1
 pytest>=7.3.2
 pytest-cov
 pytest-xdist>=3.4.0