WASHINGTON (AFP) - The United States candidly said Monday it would not immediately cut military aid to Egypt because doing so would not be in its own interest, and pledged to take its time to decide whether a coup had taken place.

The White House made clear that such a determination - which could legally compel a freezing of US$1.5 billion (S$1.9 billion) in annual military and economic aid - could depend on how the military behaves going forward.

In the most detailed public reactions so far to the overthrow of president Mohamed Mursi after just a year in office, the Obama administration called for "maximum" restraint from Egypt's armed forces following days of bloody violence.

And, as it faced accusations of playing both sides in the polarised political conflict, it condemned "explicit" calls to violence by Morsi's Muslim Brotherhood after 51 people were shot dead on Monday at a pro-Mursi demonstration.

"We remain deeply concerned about the increasing violence across Egypt. We strongly condemn any violence or any incitement to violence," State Department spokesman Jen Psaki told reporters.

She said Washington expresses "our condolences for those who have been killed" and calls on the military "to use maximum restraint."

"Egypt's stability and democratic political order are at stake," she said, calling on the Muslim Brotherhood to "engage in the process" of forming a new, stable government.

White House spokesman Jay Carney condemned what he said were "explicit calls to violence by the Muslim Brotherhood." Both officials said Washington had not yet determined whether last week's ouster of Mr Mursi by the military was a coup, as the Brotherhood claims, or part of a popular revolt against a failed government, as supporters insist.

Washington was going "to take the time necessary to review what has taken place and to monitor efforts by Egyptian authorities to forge an inclusive and democratic way forward," Mr Carney said.

But he stressed it would "not be in our best interests" to immediately cut off aid to such an important regional ally - one of two Arab nations that has a peace treaty with Israel and which helps guard the strategic Suez canal.

His remarks implied that the United States might try to use the aid to ensure the military keeps its promise of a swift handover to an interim civilian government to pave the way for new elections.

Washington has so far failed to take a position on the toppling of Mr Mursi - who had proved an uneasy US ally - aware that many Egyptians believe the Islamist leader had squandered aspirations for true democracy after three decades of rule by strongman Hosni Mubarak.

"There are millions of people on the ground who do not think it was a coup. We factor lots of factors in," said Ms Psaki.

"So we aren't taking sides because we don't think that is in the interests of Egypt and the interest of moving this process forward towards stability." But she insisted the United States was not condoning any one action in Egypt taken in recent days.

"I don't think we see the benefit of inserting the US view in a situation that continues to be volatile," she said, adding that the American role was to help Egypt "move toward stability."

Top administration officials including Secretary of State John Kerry have been in almost constant touch over the weekend with Egyptian leaders of all stripes, and there have also been contacts with the Muslim Brotherhood.

However, Ms Psaki said Washington was not calling for the military to release Mr Mursi who is under house arrest and has not been seen in public since Wednesday.

The US was not taking "positions on specific case," she said, adding "of course, we have been very publicly and privately expressing concern about arbitrary arrests."

Republican Senator John McCain on Monday renewed his call to suspend the US aid, saying it was hard to conclude that "what happened was anything other than a coup."

"This is an incredibly difficult decision, but we have to learn the lessons of history and remain true to our values." But Democratic Senator Tim Kaine said it was important "not to shoot from the hip."

During a tour by a congressional delegation last week, they heard from regional allies like UAE and Jordan "that they believe... that any sort of immediate cessation of aid would be a mistake," he said.