diff --git a/cython-3.1.2.tar.gz b/cython-3.1.2.tar.gz
deleted file mode 100644
index 907f0a0..0000000
--- a/cython-3.1.2.tar.gz
+++ /dev/null
@@ -1,3 +0,0 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:6bbf7a953fa6762dfecdec015e3b054ba51c0121a45ad851fa130f63f5331381
-size 3184825
diff --git a/cython-3.1.3.tar.gz b/cython-3.1.3.tar.gz
new file mode 100644
index 0000000..391e1ec
--- /dev/null
+++ b/cython-3.1.3.tar.gz
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:10ee785e42328924b78f75a74f66a813cb956b4a9bc91c44816d089d5934c089
+size 3186689
diff --git a/python-Cython.changes b/python-Cython.changes
index 873577c..09d30f2 100644
--- a/python-Cython.changes
+++ b/python-Cython.changes
@@ -1,3 +1,21 @@
+-------------------------------------------------------------------
+Wed Aug 13 12:01:11 UTC 2025 - Markéta Machová <mmachova@suse.com>
+
+- Update to 3.1.3
+  * Some method calls with 0 or 1 argument failed to use PyObject_VectorCallMethod().
+  * Walrus assignments of literal Python integers could generate invalid C code.
+  * cython.pythread_type_lock (also used as fallback for cython.pymutex) could stall
+    on heavily contended locks.
+  * C string arrays (not pointers) always coerced to the Python default string type,
+    even on explicit casts to other string types.
+  * Unterminated \N{} character escapes in strings could unrail the parser.
+  * An internal C function was not marked as static and leaked a linker symbol.
+  * Some Unicode letters were not recognised as lexically valid name parts.
+  * Compatibility with PyPy3.8 was lost by accident.
+  * The Linux binary wheels of 3.1.2 used SSSE3 CPU instructions which are not
+    available on some CPUs.
+- Convert to libalternatives on SLE-16-based and newer systems only
+
 -------------------------------------------------------------------
 Mon Jul 14 10:19:55 UTC 2025 - ecsos <ecsos@opensuse.org>
 
diff --git a/python-Cython.spec b/python-Cython.spec
index 24f4217..bd4a1cc 100644
--- a/python-Cython.spec
+++ b/python-Cython.spec
@@ -17,15 +17,20 @@
 
 
 %bcond_with test
+%if 0%{?suse_version} > 1500
+%bcond_without libalternatives
+%else
+%bcond_with libalternatives
+%endif
 %{?sle15_python_module_pythons}
 Name:           python-Cython
-Version:        3.1.2
+Version:        3.1.3
 Release:        0
 Summary:        The Cython compiler for writing C extensions for the Python language
 License:        Apache-2.0
 URL:            https://cython.org/
 # SourceRepository: https://github.com/cython/cython
-Source:         https://files.pythonhosted.org/packages/source/C/Cython/cython-%{version}.tar.gz
+Source:         https://files.pythonhosted.org/packages/source/c/cython/cython-%{version}.tar.gz
 Source1:        python-Cython-rpmlintrc
 BuildRequires:  %{python_module devel >= 3.8}
 BuildRequires:  %{python_module pip}
@@ -35,11 +40,16 @@ BuildRequires:  fdupes
 BuildRequires:  gcc-c++
 BuildRequires:  python-rpm-macros
 Requires:       python-devel >= 3.8
-Requires(post): update-alternatives
-Requires(postun): update-alternatives
 Conflicts:      python-Cython < 3
 Provides:       python-Cython3 = %{version}
 Obsoletes:      python-Cython3 < %{version}
+%if %{with libalternatives}
+BuildRequires:  alts
+Requires:       alts
+%else
+Requires(post): update-alternatives
+Requires(postun): update-alternatives
+%endif
 %python_subpackages
 
 %description
@@ -66,6 +76,7 @@ export CFLAGS="%{optflags} -fno-strict-aliasing"
 for p in cython cythonize cygdb ; do
     %python_clone -a %{buildroot}%{_bindir}/$p
 done
+%python_group_libalternatives cython cythonize cygdb
 
 %{python_expand chmod a+x %{buildroot}%{$python_sitearch}/Cython/Build/Cythonize.py
 sed -i "s|^#!%{_bindir}/env python$|#!%{__$python}|" %{buildroot}%{$python_sitearch}/Cython/Build/Cythonize.py
@@ -81,6 +92,9 @@ $python runtests.py -v
 }
 %endif
 
+%pre
+%python_libalternatives_reset_alternative cython
+
 %post
 %python_install_alternative cython cythonize cygdb