diff --git a/ggml/src/ggml-cuda/common.cuh b/ggml/src/ggml-cuda/common.cuh
index 7d14ce906..2e78ae4fa 100644
--- a/ggml/src/ggml-cuda/common.cuh
+++ b/ggml/src/ggml-cuda/common.cuh
@@ -329,6 +329,12 @@ static bool fp16_mma_hardware_available(const int cc) {
         (GGML_CUDA_CC_IS_MTHREADS(cc) && cc >= GGML_CUDA_CC_QY2);
 }
 
+// To be used for feature selection of external libraries, e.g. cuBLAS.
+static bool fast_bf16_hardware_available(const int cc) {
+        return (GGML_CUDA_CC_IS_AMD(cc) && (cc >= GGML_CUDA_CC_RDNA3 || GGML_CUDA_CC_IS_CDNA(cc)))
+            || (GGML_CUDA_CC_IS_NVIDIA(cc) && cc >= GGML_CUDA_CC_AMPERE);
+}
+
 static bool bf16_mma_hardware_available(const int cc) {
     return (GGML_CUDA_CC_IS_NVIDIA(cc) && cc >= GGML_CUDA_CC_AMPERE) ||
         GGML_CUDA_CC_IS_CDNA(cc) || cc >= GGML_CUDA_CC_RDNA3 ||
diff --git a/ggml/src/ggml-cuda/ggml-cuda.cu b/ggml/src/ggml-cuda/ggml-cuda.cu
index 5ae3b8d22..790553888 100644
--- a/ggml/src/ggml-cuda/ggml-cuda.cu
+++ b/ggml/src/ggml-cuda/ggml-cuda.cu
@@ -1620,11 +1620,19 @@ static void ggml_cuda_mul_mat_cublas_impl(ggml_backend_cuda_context & ctx, const
 }
 
 static void ggml_cuda_mul_mat_cublas(ggml_backend_cuda_context & ctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst) {
+    const int cc = ggml_cuda_info().devices[ctx.device].cc;
     ggml_type compute_type = src0->type;
     if (ggml_is_quantized(compute_type)) {
-        compute_type = fast_fp16_hardware_available(ggml_cuda_info().devices[ctx.device].cc) ? GGML_TYPE_F16 : GGML_TYPE_F32;
-    } else if (compute_type == GGML_TYPE_F16 && !fast_fp16_hardware_available(ggml_cuda_info().devices[ctx.device].cc)) {
+        compute_type = fast_fp16_hardware_available(cc) ? GGML_TYPE_F16 : GGML_TYPE_F32;
+    } else if (compute_type == GGML_TYPE_F16 && !fast_fp16_hardware_available(cc)) {
         compute_type = GGML_TYPE_F32;
+    } else if (compute_type == GGML_TYPE_BF16 && !fast_bf16_hardware_available(cc)) {
+        if (GGML_CUDA_CC_IS_AMD(cc) && src1->ne[1] > 32) {
+            compute_type = GGML_TYPE_F32;
+        }
+        if (GGML_CUDA_CC_IS_NVIDIA(cc) && src1->ne[1] > (cc >= GGML_CUDA_CC_VOLTA ? 8 : 128)) {
+            compute_type = GGML_TYPE_F32;
+        }
     }
     if (dst->op_params[0] == GGML_PREC_F32) {
         compute_type = GGML_TYPE_F32;