Sens. John McCain and Lindsey O. Graham urged Egypt’s military and Islamists on Tuesday to reconcile and avoid further bloodshed or risk dragging Egypt toward civil war.

The two Republicans are frequent critics of the Obama administration on foreign policy but went to Egypt to reinforce the U.S. argument that the interim leadership must negotiate with backers of ousted president Mohamed Morsi and end a stalemate now in its second month.

“We advised the existing government to release some of the Muslim Brotherhood prisoners they are holding as a gesture to try to get negotiations started between them,” McCain said in an interview as he left the country Tuesday.

The two pressed the argument with Egypt’s interim military-backed leaders that patience is running out in both political parties in Congress, McCain said, an implicit threat that some U.S. aid could eventually be withheld, even over the objection of the White House.

McCain (Ariz.) and Graham (S.C.) had earlier lobbied Congress to cut off Egypt’s $1.3 billion in annual military aid after the coup that ousted Morsi from power. But on Tuesday, the senators appeared to signal a shift in that position.

“There are some in Congress who want to sever this relationship,” Graham said at a news conference in Cairo. “We want to maintain it because it is so important to our two nations.”

Morsi and Brotherhood aides have been held virtually incommunicado since a July 3 military coup. Morsi’s followers in the Muslim Brotherhood called Tuesday for a “million man” march, and negotiations to reconcile the two sides appeared locked in a stalemate.

McCain said Muslim Brotherhood leaders they saw insisted that Morsi be released before any negotiations could begin, a position McCain said is unrealistic.

“Our impression is that is not going to happen” very soon, McCain said of Morsi’s release.

Egypt has seen a flurry of diplomatic visits by U.S., European and Arab officials in recent days in efforts to warn against violence as Egypt’s security forces prepare to break up two pro-Morsi sit-ins that have shut down roads and neighborhoods in the capital for five weeks.

McCain and Graham said Tuesday that they had not come to Egypt to broker a deal, and McCain said in the interview that he is not certain Morsi would take one if offered.

“In a democracy, you have to sit down and talk to each other even if you may not like the other person on the other side of the table,” Graham said. “You cannot talk to someone if that person is in jail.”

Last week, European Union envoy Catherine Ashton and an African delegation separately visited Morsi in detention and conveyed messages to his supporters and opponents, but they left without reaching a deal.

Muslim Brotherhood members have said publicly that they will not shut down their sprawling protest encampments until Morsi is reinstated. But analysts and liberal politicians participating in the interim government have said that the group is privately inching toward a deal, provided Morsi is allowed a more graceful, face-saving exit.

Nader al-Bakkar, a spokesman for the hard-line Salafist Nour party, which has been involved in a number of the closed-door meetings, said Tuesday that he believed a solution could be reached “in the coming days.”

The Brotherhood needs guarantees from the military that it will be able to play a role in Egyptian politics, Bakkar said.

Health officials say that more than 250 people have been killed in more than a month of unrest since the coup. Egyptian security forces killed more than 80 people when they opened fire on pro-Morsi protesters, sparking clashes late last month, in the single deadliest attack by security forces since the 2011 uprising that ousted Hosni Mubarak.

Morsi’s supporters and rights groups warn that a forceful government attempt to break up the sit-ins, which include hundreds of women and children, could result in a massacre.

“If 400 more die, it will be very difficult to put this country back on track,” Graham said.

“We had our own civil war — it started in my state,” he added. “Learn from our mistakes.”

The Tamarod — or “rebel” — movement that helped rally hundreds of thousands of Egyptians into the streets on June 30 to call for Morsi’s ouster said Tuesday that it had refused an invitation to talk to the visiting senators.

“We are bored with the big number of foreign visits to Egypt,” one of the group’s founders, Mahmoud Badr, wrote on his Facebook page. “We demand that the international community leave the Egyptians alone to determine their destiny and choices."

Sharaf al-Hourani contributed to this report.