Two senior U.S. senators visiting Cairo urged both sides in Egypt's political crisis on Tuesday to start a national dialogue and avoid violence amid intensifying diplomatic efforts to resolve the bloody stand-off.

Republicans Lindsey Graham and John McCain, dispatched by U.S. President Barack Obama to help resolve the crisis sparked by the army's overthrow of elected Islamist President Mohammed Morsi last month, also called for the release of political prisoners.

After talks with Egypt's new rulers and civil society, they told a news conference it would wrong to cut off U.S. military assistance to Egypt, worth some $1.5 billion a year, for now in reaction to Morsi's removal, despite a U.S. law that mandates suspending aid in case of coup. "Cutting off aid would be the wrong signal at the wrong time," McCain said.

They met army chief General Abdel Fattah al-Sisi, interim Vice President Mohamed ElBaradei and interim Prime Minister Hazem el-Beblawi on a mission reflecting Washington's anxiety at events in Egypt, a bulwark of its Middle East policy and the first Arab state to make peace with Israel.

McCain said they had also met members of Morsi's Freedom and Justice Party, political arm of the Muslim Brotherhood, which the senators said should be involved in a national dialogue.

Graham summed up Washington's unease in dealing with the new authorities, saying: "The people who are in charge were not elected. The people who were elected are in jail. The status quo is not acceptable."

The state news agency MENA said only that the two sides exchanged views on political developments and discussed efforts to end "the state of political polarization."

Egypt has been dangerously divided since the overthrow of Morsi on July 3 following huge demonstrations against his rule.

Morsi became Egypt's first freely-elected president in June 16, 2012, months after the overthrow of U.S.-backed strongman Hosni Mubarak, who had ruled for nearly 30 years. The ousted head of state is now being detained at an undisclosed location.

Thousands of his supporters remain camped out in two protest sites in Cairo which the government has pledged to break up.

Almost 300 people have been killed in political violence since Morsi's overthrow, including 80 shot dead by security forces in a single incident on July 27.

A diplomatic push led by the envoys from the United States, the European Union, Qatar and the United Arab Emirates has so far helped to hold off further bloodshed between Morsi's backers and the security forces but not achieved a breakthrough.

"Things should move soon, otherwise we shall miss this opportunity. This is all still incredibly fragile," said a source involved in the diplomatic initiative.

Before leaving Washington, Graham had said the Egyptian military must back out of politics quickly or risk a cut-off of military aid from Washington.

The crisis has put U.S. policy in quandary. Mubarak was close ally who kept Islamist militants under heel and maintained peace with Israel. Washington was slow to support the popular uprising that ousted him.

It cautiously welcomed the election of Morsi, an Islamist and member of the Muslim Brotherhood, and until the last minute U.S. Ambassador Anne Patterson was urging Egyptians to use the ballot box rather than street action to express their views.

Fears that Morsi was trying to establish an Islamist autocracy, coupled with a failure to ease economic hardships afflicting most of Egypt's 84 million people, led to huge street demonstrations, triggering the army move.

Washington declined to characterize the army move as a coup - a definition that would trigger an aid cut-off - and U.S. Secretary of State John Kerry last week said the army had acted to restore democracy at the urging of millions of Egyptians.

Nonetheless, many supporters of the army-installed interim government believe the United States still favors Morsi.

In Tahrir Square, the center of public protest, banners accuse Obama of supporting terrorism and tell Patterson to go home. Her appointment to a new post was announced last week.

On Monday, U.S. Deputy Secretary of State William Burns and European Union envoy Bernardino Leon met jailed Brotherhood deputy leader Khairat El-Shater in the prison where he is being held.

They tried to persuade him to accept the new reality, with no realistic prospect of Morsi being reinstated, and accept a political compromise. A Brotherhood spokesman said Shater had insisted they should be talking to Morsi and the only solution was the "reversal of the coup". A source briefed by the negotiators said the meeting had been useful and constructive.

The military has laid out a plan that could see a new head of state elected in roughly nine months. The Brotherhood says it wants nothing to do with it.

Government political advisor Mostafa Hegazy said the authorities would have to deal with the protesters at the Brotherhood camps at Rabaa al-Adawiya and al-Nahda Square to create the right conditions for the transition plan.

"The crowds exist not to find a solution or to enter political life but to disrupt everyday life and endanger the future of the nation," he told MENA. "They need to renounce violence and stop carrying weapons."

The security forces have promised the protesters safe exit if they quit the camps but have warned their patience is limited.

It is thought unlikely that they would take action before Sunday, the end of Eid al-Fitr, the holiday that marks the close of the Muslim fasting month of Ramadan.