diff --git a/Algebraic_kernel_d/include/CGAL/RS/rs2_calls.h b/Algebraic_kernel_d/include/CGAL/RS/rs2_calls.h
index d87e406e611..b45995466ac 100644
--- a/Algebraic_kernel_d/include/CGAL/RS/rs2_calls.h
+++ b/Algebraic_kernel_d/include/CGAL/RS/rs2_calls.h
@@ -35,7 +35,7 @@
 #define CGALRS_PTR(a)   void *a
 #endif
 
-// RS3 does not work with MPFR 3.1.3 to 3.1.5. In case RS3 is enabled and
+// RS3 does not work with MPFR 3.1.3 to 3.1.6. In case RS3 is enabled and
 // the version of MPFR is one of those buggy versions, abort the compilation
 // and instruct the user to update MPFR or don't use RS3.
 #ifdef CGAL_USE_RS3
@@ -43,8 +43,8 @@
 BOOST_STATIC_ASSERT_MSG(
         MPFR_VERSION_MAJOR!=3 ||
         MPFR_VERSION_MINOR!=1 ||
-        MPFR_VERSION_PATCHLEVEL<3 || MPFR_VERSION_PATCHLEVEL>5,
-        "RS3 does not work with MPFR versions 3.1.3 to 3.1.5. "#
+        MPFR_VERSION_PATCHLEVEL<3 || MPFR_VERSION_PATCHLEVEL>6,
+        "RS3 does not work with MPFR versions 3.1.3 to 3.1.6. "
         "Please update MPFR or disable RS3.");
 #endif // CGAL_USE_RS3
 
diff --git a/Installation/cmake/modules/FindMPFI.cmake b/Installation/cmake/modules/FindMPFI.cmake
index 630227c99d5..2b0f903ea2d 100644
--- a/Installation/cmake/modules/FindMPFI.cmake
+++ b/Installation/cmake/modules/FindMPFI.cmake
@@ -1,6 +1,6 @@
 find_package( GMP QUIET )
 
-if( GMP_FOUND )
+if( GMP_FOUND AND MPFR_FOUND )
 
   if( MPFI_INCLUDE_DIR AND MPFI_LIBRARIES )
     set( MPFI_FOUND TRUE )
@@ -32,14 +32,36 @@ if( GMP_FOUND )
 
   include(FindPackageHandleStandardArgs)
 
-  find_package_handle_standard_args(MPFI "DEFAULT_MSG" MPFI_LIBRARIES MPFI_INCLUDE_DIR )
+  find_package_handle_standard_args( MPFI
+                                     "DEFAULT_MSG"
+                                     MPFI_LIBRARIES
+                                     MPFI_INCLUDE_DIR )
 
-else( GMP_FOUND )
+else( GMP_FOUND AND MPFR_FOUND )
 
   message( STATUS "MPFI needs GMP and MPFR" )
 
-endif( GMP_FOUND )
+endif( GMP_FOUND AND MPFR_FOUND )
 
 if( MPFI_FOUND )
-  set( MPFI_USE_FILE "CGAL_UseMPFI" )
+  get_dependency_version( MPFR )
+  IS_VERSION_LESS("${MPFR_VERSION}" "4.0.0" _MPFR_OLD)
+
+  get_dependency_version( MPFI )
+  IS_VERSION_LESS("${MPFI_VERSION}" "1.5.2" _MPFI_OLD)
+
+  if( ( _MPFR_OLD AND NOT _MPFI_OLD ) OR ( NOT _MPFR_OLD AND _MPFI_OLD ) )
+
+    message(
+      STATUS
+      "MPFI<1.5.2 requires MPFR<4.0.0; MPFI>=1.5.2 requires MPFR>=4.0.0" )
+
+    set( MPFI_FOUND FALSE )
+
+  else( ( _MPFR_OLD AND NOT _MPFI_OLD ) OR ( NOT _MPFR_OLD AND _MPFI_OLD ) )
+
+    set( MPFI_USE_FILE "CGAL_UseMPFI" )
+
+  endif( ( _MPFR_OLD AND NOT _MPFI_OLD ) OR ( NOT _MPFR_OLD AND _MPFI_OLD ) )
+
 endif( MPFI_FOUND )