Index: libomptarget/deviceRTLs/nvptx/src/libcall.cu
===================================================================
--- libomptarget/deviceRTLs/nvptx/src/libcall.cu
+++ libomptarget/deviceRTLs/nvptx/src/libcall.cu
@@ -164,7 +164,8 @@
   if (isRuntimeUninitialized()) {
     ASSERT0(LT_FUSSY, isSPMDMode(),
             "Expected SPMD mode only with uninitialized runtime.");
-    return parallelLevel;
+    // parallelLevel starts from 0, need to add 1 for correct level.
+    return parallelLevel + 1;
   }
   int level = 0;
   omptarget_nvptx_TaskDescr *currTaskDescr =
Index: libomptarget/deviceRTLs/nvptx/src/loop.cu
===================================================================
--- libomptarget/deviceRTLs/nvptx/src/loop.cu
+++ libomptarget/deviceRTLs/nvptx/src/loop.cu
@@ -205,8 +205,12 @@
   INLINE static void dispatch_init(kmp_Ident *loc, int32_t threadId,
                                    kmp_sched_t schedule, T lb, T ub, ST st,
                                    ST chunk) {
-    ASSERT0(LT_FUSSY, checkRuntimeInitialized(loc),
-            "Expected non-SPMD mode + initialized runtime.");
+    if (checkRuntimeUninitialized(loc)) {
+      // In SPMD mode no need to check parallelism level - dynamic scheduling
+      // may appear only in L2 parallel regions with lightweight runtime.
+      ASSERT0(LT_FUSSY, checkSPMDMode(loc), "Expected non-SPMD mode.");
+      return;
+    }
     int tid = GetLogicalThreadIdInBlock(checkSPMDMode(loc));
     omptarget_nvptx_TaskDescr *currTaskDescr = getMyTopTaskDescriptor(tid);
     T tnum = currTaskDescr->ThreadsInTeam();
@@ -439,8 +443,15 @@
 
   INLINE static int dispatch_next(kmp_Ident *loc, int32_t gtid, int32_t *plast,
                                   T *plower, T *pupper, ST *pstride) {
-    ASSERT0(LT_FUSSY, checkRuntimeInitialized(loc),
-            "Expected non-SPMD mode + initialized runtime.");
+    if (checkRuntimeUninitialized(loc)) {
+      // In SPMD mode no need to check parallelism level - dynamic scheduling
+      // may appear only in L2 parallel regions with lightweight runtime.
+      ASSERT0(LT_FUSSY, checkSPMDMode(loc), "Expected non-SPMD mode.");
+      if (*plast)
+        return DISPATCH_FINISHED;
+      *plast = 1;
+      return DISPATCH_NOTFINISHED;
+    }
     // ID of a thread in its own warp
 
     // automatically selects thread or warp ID based on selected implementation
Index: libomptarget/deviceRTLs/nvptx/src/parallel.cu
===================================================================
--- libomptarget/deviceRTLs/nvptx/src/parallel.cu
+++ libomptarget/deviceRTLs/nvptx/src/parallel.cu
@@ -407,7 +407,7 @@
   if (checkRuntimeUninitialized(loc)) {
     ASSERT0(LT_FUSSY, checkSPMDMode(loc),
             "Expected SPMD mode with uninitialized runtime.");
-    return parallelLevel;
+    return parallelLevel + 1;
   }
 
   int threadId = GetLogicalThreadIdInBlock(checkSPMDMode(loc));
Index: libomptarget/test/offloading/spmd_parallel_regions.cpp
===================================================================
--- /dev/null
+++ libomptarget/test/offloading/spmd_parallel_regions.cpp
@@ -0,0 +1,34 @@
+// RUN: %libomptarget-compilexx-run-and-check-aarch64-unknown-linux-gnu
+// RUN: %libomptarget-compilexx-run-and-check-powerpc64-ibm-linux-gnu
+// RUN: %libomptarget-compilexx-run-and-check-powerpc64le-ibm-linux-gnu
+// RUN: %libomptarget-compilexx-run-and-check-x86_64-pc-linux-gnu
+// RUN: %libomptarget-compilexx-run-and-check-nvptx64-nvidia-cuda
+
+#include <stdio.h>
+#include <omp.h>
+
+int main(void) {
+  int isHost = -1;
+  int ParallelLevel1, ParallelLevel2 = -1;
+
+#pragma omp target parallel map(from: isHost, ParallelLevel1, ParallelLevel2)
+  {
+    isHost = omp_is_initial_device();
+    ParallelLevel1 = omp_get_level();
+#pragma omp parallel for schedule(dynamic) lastprivate(ParallelLevel2)
+    for (int I = 0; I < 10; ++I)
+      ParallelLevel2 = omp_get_level();
+  }
+
+  if (isHost < 0) {
+    printf("Runtime error, isHost=%d\n", isHost);
+  }
+
+  // CHECK: Target region executed on the device
+  printf("Target region executed on the %s\n", isHost ? "host" : "device");
+  // CHECK: Parallel level in SPMD mode: L1 is 1, L2 is 2
+  printf("Parallel level in SPMD mode: L1 is %d, L2 is %d\n", ParallelLevel1,
+         ParallelLevel2);
+
+  return isHost;
+}