diff --git a/ggml/src/ggml-cuda/argsort.cu b/ggml/src/ggml-cuda/argsort.cu
index c4f08091e79a..33a38c23e87e 100644
--- a/ggml/src/ggml-cuda/argsort.cu
+++ b/ggml/src/ggml-cuda/argsort.cu
@@ -28,6 +28,20 @@ static __global__ void init_offsets(int * offsets, const int ncols, const int nr
 #endif  // STRIDED_ITERATOR_AVAILABLE
 
 #ifdef GGML_CUDA_USE_CUB
+
+// returns the suggested maximum number of rows to process during one argsort_f32_i32_cuda_cub() call
+int argsort_f32_i32_cuda_cub_chunk_nrows(const size_t nb01, const int64_t nrows) {
+    // perform argsort in chunks up to approximately this size (currently 64MB)
+    // to avoid excessive temporary buffers memory usage
+    const int chunk_bytes = 1 << 26;
+
+    // calculate how many rows will fit in one chunk (must be at least one)
+    const int chunk_nrows = chunk_bytes > nb01 ? chunk_bytes / nb01 : 1;
+
+    // limit the resulting amount to total nrows
+    return nrows < chunk_nrows ? nrows : chunk_nrows;
+}
+
 void argsort_f32_i32_cuda_cub(ggml_cuda_pool & pool,
                               const float *    x,
                               int *            dst,
@@ -254,11 +268,22 @@ void ggml_cuda_op_argsort(ggml_backend_cuda_context & ctx, ggml_tensor * dst) {
     const size_t shared_mem     = ncols_pad * sizeof(int);
     const size_t max_shared_mem = ggml_cuda_info().devices[ggml_cuda_get_device()].smpb;
 
-    if (shared_mem > max_shared_mem || ncols > 1024) {
-        ggml_cuda_pool & pool = ctx.pool();
-        argsort_f32_i32_cuda_cub(pool, src0_d, (int *) dst_d, ncols, nrows, order, stream);
-    } else {
-        argsort_f32_i32_cuda_bitonic(src0_d, (int *) dst_d, ncols, nrows, order, stream);
+    // early return if we can use bitonic argsort
+    if (shared_mem <= max_shared_mem && ncols <= 1024) {
+        return argsort_f32_i32_cuda_bitonic(src0_d, (int *) dst_d, ncols, nrows, order, stream);
+    }
+
+    const int chunk_nrows = argsort_f32_i32_cuda_cub_chunk_nrows(src0->nb[1], nrows);
+
+    ggml_cuda_pool & pool = ctx.pool();
+
+    for (int64_t i = 0; i < nrows; i += chunk_nrows) {
+        int iter_nrows = chunk_nrows < nrows - i ? chunk_nrows : nrows - i;
+
+        argsort_f32_i32_cuda_cub(pool, src0_d, (int *) dst_d, ncols, iter_nrows, order, stream);
+
+        src0_d += ncols * iter_nrows;
+        dst_d  += ncols * iter_nrows;
     }
 #else
     argsort_f32_i32_cuda_bitonic(src0_d, (int *) dst_d, ncols, nrows, order, stream);
diff --git a/ggml/src/ggml-cuda/argsort.cuh b/ggml/src/ggml-cuda/argsort.cuh
index 22b7306f2020..3abb6448a057 100644
--- a/ggml/src/ggml-cuda/argsort.cuh
+++ b/ggml/src/ggml-cuda/argsort.cuh
@@ -3,6 +3,7 @@
 void ggml_cuda_op_argsort(ggml_backend_cuda_context & ctx, ggml_tensor * dst);
 
 #ifdef GGML_CUDA_USE_CUB
+int argsort_f32_i32_cuda_cub_chunk_nrows(const size_t nb01, const int64_t nrows);
 void argsort_f32_i32_cuda_cub(ggml_cuda_pool & pool,
                               const float *    x,
                               int *            dst,
diff --git a/ggml/src/ggml-cuda/top-k.cu b/ggml/src/ggml-cuda/top-k.cu
index db1d39e2dc71..5e708e6c5ed4 100644
--- a/ggml/src/ggml-cuda/top-k.cu
+++ b/ggml/src/ggml-cuda/top-k.cu
@@ -75,17 +75,26 @@ void ggml_cuda_op_top_k(ggml_backend_cuda_context & ctx, ggml_tensor * dst) {
     const int    ncols_pad      = next_power_of_2(ncols);
     const size_t shared_mem     = ncols_pad * sizeof(int);
     const size_t max_shared_mem = ggml_cuda_info().devices[ggml_cuda_get_device()].smpb;
+    const bool   use_bitonic    = shared_mem <= max_shared_mem && ncols <= 1024;
+    const int    chunk_nrows    = argsort_f32_i32_cuda_cub_chunk_nrows(src0->nb[1], nrows);
 
-    ggml_cuda_pool_alloc<int> temp_dst_alloc(pool, ncols * nrows);
+    ggml_cuda_pool_alloc<int> temp_dst_alloc(pool, ncols * chunk_nrows);
     int *                     tmp_dst = temp_dst_alloc.get();
 
-    if (shared_mem > max_shared_mem || ncols > 1024) {
-        argsort_f32_i32_cuda_cub(pool, src0_d, tmp_dst, ncols, nrows, GGML_SORT_ORDER_DESC, stream);
-    } else {
-        argsort_f32_i32_cuda_bitonic(src0_d, tmp_dst, ncols, nrows, GGML_SORT_ORDER_DESC, stream);
+    for (int64_t i = 0; i < nrows; i += chunk_nrows) {
+        int iter_nrows = chunk_nrows < nrows - i ? chunk_nrows : nrows - i;
+
+        if (use_bitonic) {
+            argsort_f32_i32_cuda_bitonic(src0_d, tmp_dst, ncols, iter_nrows, GGML_SORT_ORDER_DESC, stream);
+        } else {
+            argsort_f32_i32_cuda_cub(pool, src0_d, tmp_dst, ncols, iter_nrows, GGML_SORT_ORDER_DESC, stream);
+        }
+        CUDA_CHECK(cudaMemcpy2DAsync(dst_d, k * sizeof(int), tmp_dst, ncols * sizeof(int), k * sizeof(int), iter_nrows,
+                                     cudaMemcpyDeviceToDevice, stream));
+
+        src0_d += ncols * iter_nrows;
+        dst_d  += k     * iter_nrows;
     }
-    CUDA_CHECK(cudaMemcpy2DAsync(dst_d, k * sizeof(int), tmp_dst, ncols * sizeof(int), k * sizeof(int), nrows,
-                                 cudaMemcpyDeviceToDevice, stream));
 #else                             // GGML_CUDA_USE_CUB
     ggml_cuda_pool_alloc<int> temp_dst_alloc(pool, ncols * nrows);
     int *                     tmp_dst = temp_dst_alloc.get();