diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 9b836cd6d6..1a4387ee5b 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -538,6 +538,10 @@ jobs:
     name: ${{ matrix.configuration.job_name }}
     # See: https://github.com/actions/runner-images#available-images.
     runs-on: windows-2022
+    defaults:
+      run:
+        # Enforce fail-fast behavior for PowerShell.
+        shell: pwsh -Command "$PSNativeCommandUseErrorActionPreference = $true; $ErrorActionPreference = 'Stop'; & '{0}'"
 
     strategy:
       fail-fast: false
@@ -570,7 +574,13 @@ jobs:
       - *CHECKOUT
 
       - name: Generate buildsystem
-        run: cmake -E env CFLAGS="/WX ${{ matrix.configuration.cpp_flags }}" cmake -B build -DSECP256K1_ENABLE_MODULE_RECOVERY=ON -DSECP256K1_BUILD_EXAMPLES=ON ${{ matrix.configuration.cmake_options }}
+        run: |
+          cmake -E env CFLAGS="/WX ${{ matrix.configuration.cpp_flags }}" `
+          cmake -B build `
+            -DSECP256K1_BUILD_PRECOMPUTED=ON `
+            -DSECP256K1_ENABLE_MODULE_RECOVERY=ON `
+            -DSECP256K1_BUILD_EXAMPLES=ON `
+            ${{ matrix.configuration.cmake_options }}
 
       - name: Build
         run: cmake --build build --config RelWithDebInfo -- /p:UseMultiToolTask=true /maxCpuCount
@@ -596,6 +606,11 @@ jobs:
           build\bin\RelWithDebInfo\bench_internal.exe
           build\bin\RelWithDebInfo\bench.exe
 
+      - name: Check precomputed files
+        run: |
+          cmake -E copy build/src/precomputed_ecmult.c build/src/precomputed_ecmult_gen.c -t src
+          git diff --exit-code
+
   win64-native-headers:
     name: "x64 (MSVC): C++ (public headers)"
     # See: https://github.com/actions/runner-images#available-images.
diff --git a/CMakeLists.txt b/CMakeLists.txt
index a84305c340..1e7caaed94 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -1,5 +1,11 @@
 cmake_minimum_required(VERSION 3.22)
 
+if(POLICY CMP0171)
+  # `codegen` is a reserved target name.
+  # See: https://cmake.org/cmake/help/latest/policy/CMP0171.html
+  cmake_policy(SET CMP0171 NEW)
+endif()
+
 #=============================
 # Project / Package metadata
 #=============================
@@ -141,6 +147,11 @@ option(SECP256K1_BUILD_EXHAUSTIVE_TESTS "Build exhaustive tests." ON)
 option(SECP256K1_BUILD_CTIME_TESTS "Build constant-time tests." ${SECP256K1_VALGRIND})
 option(SECP256K1_BUILD_EXAMPLES "Build examples." OFF)
 
+option(SECP256K1_BUILD_PRECOMPUTED "Generate the precomputed files in the build tree." OFF)
+if(SECP256K1_BUILD_PRECOMPUTED AND CMAKE_CROSSCOMPILING)
+  message(FATAL_ERROR "SECP256K1_BUILD_PRECOMPUTED requires executing precompute tools, which is not supported when cross compiling.")
+endif()
+
 # Redefine configuration flags.
 # We leave assertions on, because they are only used in the examples, and we want them always on there.
 if(MSVC)
diff --git a/cmake/Precompute.cmake b/cmake/Precompute.cmake
new file mode 100644
index 0000000000..7192af637b
--- /dev/null
+++ b/cmake/Precompute.cmake
@@ -0,0 +1,21 @@
+function(precompute base_name)
+  add_executable(secp256k1_precompute_${base_name} EXCLUDE_FROM_ALL precompute_${base_name}.c)
+  set_target_properties(secp256k1_precompute_${base_name} PROPERTIES
+    COMPILE_DEFINITIONS VERIFY
+    RUNTIME_OUTPUT_DIRECTORY ${PROJECT_BINARY_DIR}
+  )
+  set(CODEGEN_OPT "")
+  if(POLICY CMP0171)
+    cmake_policy(GET CMP0171 _cmp0171_status)
+    if(_cmp0171_status STREQUAL "NEW")
+      set(CODEGEN_OPT CODEGEN)
+    endif()
+  endif()
+  add_custom_command(
+    OUTPUT ${PROJECT_BINARY_DIR}/src/precomputed_${base_name}.c
+    COMMAND secp256k1_precompute_${base_name}
+    DEPENDS secp256k1_precompute_${base_name}
+    WORKING_DIRECTORY ${PROJECT_BINARY_DIR}
+    ${CODEGEN_OPT}
+  )
+endfunction()
diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
index a45eeb93e4..3293e5a7e7 100644
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -45,10 +45,22 @@ if(SECP256K1_ENABLE_MODULE_ECDH)
   set_property(TARGET secp256k1 APPEND PROPERTY PUBLIC_HEADER ${PROJECT_SOURCE_DIR}/include/secp256k1_ecdh.h)
 endif()
 
-add_library(secp256k1_precomputed OBJECT EXCLUDE_FROM_ALL
-  precomputed_ecmult.c
-  precomputed_ecmult_gen.c
-)
+add_library(secp256k1_precomputed OBJECT)
+if(SECP256K1_BUILD_PRECOMPUTED)
+  include(Precompute)
+  precompute(ecmult)
+  precompute(ecmult_gen)
+  target_sources(secp256k1_precomputed PRIVATE
+    ${PROJECT_BINARY_DIR}/src/precomputed_ecmult.c
+    ${PROJECT_BINARY_DIR}/src/precomputed_ecmult_gen.c
+  )
+  target_include_directories(secp256k1_precomputed PRIVATE ${CMAKE_CURRENT_LIST_DIR})
+else()
+  target_sources(secp256k1_precomputed PRIVATE
+    ${CMAKE_CURRENT_LIST_DIR}/precomputed_ecmult.c
+    ${CMAKE_CURRENT_LIST_DIR}/precomputed_ecmult_gen.c
+  )
+endif()
 
 # Add objects explicitly rather than linking to the object libs to keep them
 # from being exported.
diff --git a/src/precompute_ecmult.c b/src/precompute_ecmult.c
index 8579c85f22..62938c9468 100644
--- a/src/precompute_ecmult.c
+++ b/src/precompute_ecmult.c
@@ -75,7 +75,7 @@ int main(void) {
     fprintf(fp, "#include \"precomputed_ecmult.h\"\n");
     fprintf(fp, "#define S(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p) SECP256K1_GE_STORAGE_CONST(0x##a##u,0x##b##u,0x##c##u,0x##d##u,0x##e##u,0x##f##u,0x##g##u,0x##h##u,0x##i##u,0x##j##u,0x##k##u,0x##l##u,0x##m##u,0x##n##u,0x##o##u,0x##p##u)\n");
     fprintf(fp, "#if ECMULT_WINDOW_SIZE > %d\n", window_g);
-    fprintf(fp, "   #error configuration mismatch, invalid ECMULT_WINDOW_SIZE. Try deleting precomputed_ecmult.c before the build.\n");
+    fprintf(fp, "   #error configuration mismatch, invalid ECMULT_WINDOW_SIZE. If this is an Autotools build, try deleting precomputed_ecmult.c before the build. If this is a CMake build, pass -DSECP256K1_BUILD_PRECOMPUTED=ON to cmake.\n");
     fprintf(fp, "#endif\n");
     fprintf(fp, "#ifdef EXHAUSTIVE_TEST_ORDER\n");
     fprintf(fp, "#    error Cannot compile precomputed_ecmult.c in exhaustive test mode\n");
diff --git a/src/precompute_ecmult_gen.c b/src/precompute_ecmult_gen.c
index a03abdb548..d09e3ffa77 100644
--- a/src/precompute_ecmult_gen.c
+++ b/src/precompute_ecmult_gen.c
@@ -90,7 +90,7 @@ int main(int argc, char **argv) {
         print_table(fp, COMB_BLOCKS, COMB_TEETH);
     }
     fprintf(fp, "#else\n");
-    fprintf(fp, "#    error Configuration mismatch, invalid COMB_* parameters. Try deleting precomputed_ecmult_gen.c before the build.\n");
+    fprintf(fp, "#    error Configuration mismatch, invalid COMB_* parameters. If this is an Autotools build, try deleting precomputed_ecmult_gen.c before the build. If this is a CMake build, pass -DSECP256K1_BUILD_PRECOMPUTED=ON to cmake.\n");
     fprintf(fp, "#endif\n");
 
     fprintf(fp, "};\n");
diff --git a/src/precomputed_ecmult.c b/src/precomputed_ecmult.c
index cbd030ce50..491c497ee5 100644
--- a/src/precomputed_ecmult.c
+++ b/src/precomputed_ecmult.c
@@ -7,7 +7,7 @@
 #include "precomputed_ecmult.h"
 #define S(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p) SECP256K1_GE_STORAGE_CONST(0x##a##u,0x##b##u,0x##c##u,0x##d##u,0x##e##u,0x##f##u,0x##g##u,0x##h##u,0x##i##u,0x##j##u,0x##k##u,0x##l##u,0x##m##u,0x##n##u,0x##o##u,0x##p##u)
 #if ECMULT_WINDOW_SIZE > 15
-   #error configuration mismatch, invalid ECMULT_WINDOW_SIZE. Try deleting precomputed_ecmult.c before the build.
+   #error configuration mismatch, invalid ECMULT_WINDOW_SIZE. If this is an Autotools build, try deleting precomputed_ecmult.c before the build. If this is a CMake build, pass -DSECP256K1_BUILD_PRECOMPUTED=ON to cmake.
 #endif
 #ifdef EXHAUSTIVE_TEST_ORDER
 #    error Cannot compile precomputed_ecmult.c in exhaustive test mode
diff --git a/src/precomputed_ecmult_gen.c b/src/precomputed_ecmult_gen.c
index 248fb077e5..6cbf37759d 100644
--- a/src/precomputed_ecmult_gen.c
+++ b/src/precomputed_ecmult_gen.c
@@ -1773,7 +1773,7 @@ S(2934de46,a6d921f8,720567e6,b46e6362,36a7ed53,483b13ed,20958452,3225accd,597969
 S(4e9991b,92fa8c4e,4e8efe45,66966073,319e80d3,a54d4b7a,b61cfcc4,7ddaa5d5,9d03ea22,21d4d80e,261952e2,73f6a8cf,c31f6091,e5aa0a8f,2281ffbf,1345df9e),
 S(ff3d6136,ffac5b0c,bfc6c5c0,c30dc01a,7ea3d56c,20bd3103,b178e3d3,ae180068,eccdc641,7b1bfff1,bf2fc8d3,2269523e,ab89890d,bffe0a19,8f594490,e7739bb8)}
 #else
-#    error Configuration mismatch, invalid COMB_* parameters. Try deleting precomputed_ecmult_gen.c before the build.
+#    error Configuration mismatch, invalid COMB_* parameters. If this is an Autotools build, try deleting precomputed_ecmult_gen.c before the build. If this is a CMake build, pass -DSECP256K1_BUILD_PRECOMPUTED=ON to cmake.
 #endif
 };
 #undef S