diff --git a/Misc/NEWS.d/next/Core and Builtins/2020-10-10-13-53-52.bpo-41993.YMzixQ.rst b/Misc/NEWS.d/next/Core and Builtins/2020-10-10-13-53-52.bpo-41993.YMzixQ.rst
new file mode 100644
index 00000000000..3669cf11ea4
--- /dev/null
+++ b/Misc/NEWS.d/next/Core and Builtins/2020-10-10-13-53-52.bpo-41993.YMzixQ.rst	
@@ -0,0 +1,2 @@
+Fixed potential issues with removing not completely initialized module from
+``sys.modules`` when import fails.
diff --git a/Python/import.c b/Python/import.c
index 505688400ef..26b80f320c3 100644
--- a/Python/import.c
+++ b/Python/import.c
@@ -902,7 +902,11 @@ PyImport_AddModule(const char *name)
 }
 
 
-/* Remove name from sys.modules, if it's there. */
+/* Remove name from sys.modules, if it's there.
+ * Can be called with an exception raised.
+ * If fail to remove name a new exception will be chained with the old
+ * exception, otherwise the old exception is preserved.
+ */
 static void
 remove_module(PyThreadState *tstate, PyObject *name)
 {
@@ -910,18 +914,17 @@ remove_module(PyThreadState *tstate, PyObject *name)
     _PyErr_Fetch(tstate, &type, &value, &traceback);
 
     PyObject *modules = tstate->interp->modules;
-    if (!PyMapping_HasKey(modules, name)) {
-        goto out;
+    if (PyDict_CheckExact(modules)) {
+        PyObject *mod = _PyDict_Pop(modules, name, Py_None);
+        Py_XDECREF(mod);
     }
-    if (PyMapping_DelItem(modules, name) < 0) {
-        _PyErr_SetString(tstate, PyExc_RuntimeError,
-                         "deleting key in sys.modules failed");
-        _PyErr_ChainExceptions(type, value, traceback);
-        return;
+    else if (PyMapping_DelItem(modules, name) < 0) {
+        if (_PyErr_ExceptionMatches(tstate, PyExc_KeyError)) {
+            _PyErr_Clear(tstate);
+        }
     }
 
-out:
-    _PyErr_Restore(tstate, type, value, traceback);
+    _PyErr_ChainExceptions(type, value, traceback);
 }