diff --git a/lms/djangoapps/instructor_task/tasks_helper.py b/lms/djangoapps/instructor_task/tasks_helper.py
index 8808db2a5a..f0ef86eb43 100644
--- a/lms/djangoapps/instructor_task/tasks_helper.py
+++ b/lms/djangoapps/instructor_task/tasks_helper.py
@@ -1421,7 +1421,11 @@ def generate_students_certificates(
     task_progress.update_task_state(extra_meta=current_step)
 
     statuses_to_regenerate = task_input.get('statuses_to_regenerate', [])
-    students_require_certs = students_require_certificate(course_id, enrolled_students, statuses_to_regenerate)
+    if students is not None and not statuses_to_regenerate:
+        # We want to skip 'filtering students' only when students are given and statuses to regenerate are not
+        students_require_certs = enrolled_students
+    else:
+        students_require_certs = students_require_certificate(course_id, enrolled_students, statuses_to_regenerate)
 
     if statuses_to_regenerate:
         # Mark existing generated certificates as 'unavailable' before regenerating
diff --git a/lms/djangoapps/instructor_task/tests/test_tasks_helper.py b/lms/djangoapps/instructor_task/tests/test_tasks_helper.py
index 6a8b087f39..5d4b5f0627 100644
--- a/lms/djangoapps/instructor_task/tests/test_tasks_helper.py
+++ b/lms/djangoapps/instructor_task/tests/test_tasks_helper.py
@@ -1650,7 +1650,7 @@ class TestCertificateGeneration(InstructorTaskModuleTestCase):
             result
         )
 
-    def test_certificate_regeneration_for_students(self):
+    def test_certificate_regeneration_for_statuses_to_regenerate(self):
         """
         Verify that certificates are regenerated for all eligible students enrolled in a course whose generated
         certificate statuses lies in the list 'statuses_to_regenerate' given in task_input.
@@ -1937,3 +1937,78 @@ class TestCertificateGeneration(InstructorTaskModuleTestCase):
              if cert.status == CertificateStatuses.unavailable and cert.grade == default_grade]
 
         self.assertEquals(len(unavailable_certificates), 2)
+
+    def test_certificate_regeneration_for_students(self):
+        """
+        Verify that certificates are regenerated for all students passed in task_input.
+        """
+        # create 10 students
+        students = [self.create_student(username='student_{}'.format(i), email='student_{}@example.com'.format(i))
+                    for i in xrange(1, 11)]
+
+        # mark 2 students to have certificates generated already
+        for student in students[:2]:
+            GeneratedCertificateFactory.create(
+                user=student,
+                course_id=self.course.id,
+                status=CertificateStatuses.downloadable,
+                mode='honor'
+            )
+
+        # mark 3 students to have certificates generated with status 'error'
+        for student in students[2:5]:
+            GeneratedCertificateFactory.create(
+                user=student,
+                course_id=self.course.id,
+                status=CertificateStatuses.error,
+                mode='honor'
+            )
+
+        # mark 6th students to have certificates generated with status 'deleted'
+        for student in students[5:6]:
+            GeneratedCertificateFactory.create(
+                user=student,
+                course_id=self.course.id,
+                status=CertificateStatuses.deleted,
+                mode='honor'
+            )
+
+        # mark 7th students to have certificates generated with status 'norpassing'
+        for student in students[6:7]:
+            GeneratedCertificateFactory.create(
+                user=student,
+                course_id=self.course.id,
+                status=CertificateStatuses.notpassing,
+                mode='honor'
+            )
+
+        # white-list 7 students
+        for student in students[:7]:
+            CertificateWhitelistFactory.create(user=student, course_id=self.course.id, whitelist=True)
+
+        current_task = Mock()
+        current_task.update_state = Mock()
+
+        # Certificates should be regenerated for students having generated certificates with status
+        # 'downloadable' or 'error' which are total of 5 students in this test case
+        task_input = {'students': [student.id for student in students]}
+
+        with patch('instructor_task.tasks_helper._get_current_task') as mock_current_task:
+            mock_current_task.return_value = current_task
+            with patch('capa.xqueue_interface.XQueueInterface.send_to_queue') as mock_queue:
+                mock_queue.return_value = (0, "Successfully queued")
+                result = generate_students_certificates(
+                    None, None, self.course.id, task_input, 'certificates generated'
+                )
+
+        self.assertDictContainsSubset(
+            {
+                'action_name': 'certificates generated',
+                'total': 10,
+                'attempted': 10,
+                'succeeded': 7,
+                'failed': 3,
+                'skipped': 0,
+            },
+            result
+        )