WASHINGTON, July 31 (Reuters) - The United States still plans to hold a major military exercise called Bright Star in Egypt in mid-September, U.S. Defense Secretary Chuck Hagel said on Wednesday, even after the Egyptian military's toppling of the president and the violence that has ensued.

"We're planning on going ahead with it," Hagel told reporters at a Pentagon news conference.

Hagel has been in regular contact with Egyptian army chief General Abdel Fattah al-Sissi since the military ousted Islamist President Mohamed Mursi on July 3.

The United States has opted against deciding whether to label Mursi's removal a "coup," something that would trigger a cut-off in aid and could alienate it from the Egyptian military, which benefits from $1.3 billion in annual U.S. military aid.

But U.S. ties with Egypt's armed forces have shown signs of strain, including President Barack Obama's decision last week to halt delivery of four F-16 fighter jets.

The joint drill, dating back to 1981, is seen as a cornerstone of U.S.-Egyptian military relations and began after the Camp David Peace Accords between Egypt and Israel.

The exercise, held every two years, was canceled in 2011 because of the political turmoil in Egypt following the ouster of longtime autocrat and U.S. ally Hosni Mubarak in a popular revolution.

A U.S. military official, speaking on condition of anonymity, told Reuters that the United States was continuing to communicate with Egyptian officials on Bright Star ahead of the exercise.

At present, the exercise was expected to be somewhat smaller than it was in 2009, the official told Reuters, without providing details.

Egypt's interim, army-backed rulers signaled on Wednesday that they could soon act to end weeks of sit-in protests, setting up a potentially bloody showdown with Mursi's Muslim Brotherhood. (Reporting by Phil Stewart; Editing by Eric Walsh)