U.S. Senators John McCain and Lindsey Graham are expected to arrive in Cairo  Monday evening, amid an international effort to defuse the crisis ignited by Egyptian President Mohammed Morsi's downfall.

U.S. President Barack Obama has asked McCain and Graham to travel to Egypt to meet members of the new government and the opposition.

News of McCain and Graham's visit comes hours after Egypt's state news agency MENA reported that Western and Arab envoys visited a high-ranking Muslim Brotherhood member in jail.

According to a top U.S. diplomat, it was U.S. Deputy Secretary of State William Burns who met with Khairat el-Shater, the powerful deputy head of the Brotherhood, the Islamist group from which Morsi hails. Burns was accompanied by the foreign ministers of Qatar and the United Arab Emirates as well as an EU envoy.

Brotherhood spokesman Gehad El-Haddad on Monday confirmed that the envoys had visitedjailed deputy Brotherhood leader Khairat El-Shater in prison inthe early hours of Monday, but he had cut the meeting short, saying they should be talking to Morsi.

Hadad said that envoys were urging the Muslim Brotherhood to "accept that the militarycoup has happened and try to recover with minimum damage"but declared "We refuse to do so," adding that there was noagreement on how to start talks.

Shater, the deputy leader of the group that propelled Morsi to office last year in Egypt's first democratic presidential election, is charged with complicity in the killing of anti-Morsi protesters. Seen as the Brotherhood's main political strategist, he was arrested after Morsi's downfall.

Hadad said that Shater told the envoys on Monday he could not speak on anyone's behalf, that Morsi was the only person who could "solve the mess" and that the only solution was "full restoration of constitutionallegitimacy and reversal of the coup".

"They invited him for discussions but he ended it abruptlysaying those three statements. Then he walked out of the room,"Haddad said, speaking by telephone.

He said Shater had passed on his account of the meeting viaa fellow Brotherhood detainee who had been allowed a family visit.

According to the BBC, Burns held separate talks with the Egypt's foreign minister, Nabil Fahmy. Also in attendance at the meeting with Fahmy was the European Union's envoy, Bernardino Leon.

Burns and the three other diplomats are in Egypt as part of international efforts to end a standoff between Mohammed Morsi's supporters and the government installed by the military after it toppled the Islamist president in a July 3 coup.

The army-backed government said on Sunday it would give mediation a chance but warned that time was limited.

In the United States, which supplies Egypt with $1.5 billion in aid each year, Graham said the Egyptian army must move "more aggressively" to hold elections. He said future U.S. aid will hinge upon a return to civilian rule.

"The military can't keep running the country. We need democratic elections," Graham said in a CNN interview.

Washington has been grappling with how to respond to the situation in Egypt, for decades an important ally in its Middle East policy.

"I want to keep the aid flowing to Egypt, but it has to be with the understanding that Egypt is going to march toward democracy, not toward a military dictatorship. And that's the message we're going to send," Graham said.