Updated

International envoys extended their visit to Cairo on Monday as efforts intensified to find a peaceful way out of the crisis sparked by the Egyptian military's overthrow of Islamist president Mohamed Morsi.

US Deputy Secretary of State William Burns met the number two of Morsi's Muslim Brotherhood movement, Khairat al-Shater, in prison, the official MENA news agency said.

The report said Burns was accompanied by EU envoy Bernardino Leon and top diplomats of Qatar and the United Arab Emirates during the visit to Shater at Cairo's high security prison in Tora.

Burns and Leon were due to fly out on Sunday night but extended their stay, an airport source said.

The powerful Shater, one of the main financiers of the Muslim Brotherhood, is due to face trial on August 25 along with senior Brotherhood leader Rashad Bayoumi and Brotherhood Supreme Guide Mohammed Badie, who is currently in hiding.

The three are accused of inciting the killing of protesters during clashes outside the Brotherhood headquarters in Cairo in June.

Morsi himself has been formally remanded in custody on suspicion of offences committed when he escaped from prison during the 2011 revolt that toppled former president Hosni Mubarak.

Burns had already met army chief Abdel Fattah al-Sisi amid intense efforts to mediate a solution to the crisis pitting Morsi loyalists and the army-backed interim leadership.

Days of heated diplomatic activity in Cairo have seen visits by Burns, EU foreign policy chief Catherine Ashton, Arab diplomats and an African Union delegation.

Supporters of Morsi -- Egypt's first freely elected president-- see his ouster by the military as a violation of democracy and insist on nothing short of reinstatement.

The interim leaders however say there is no turning back on the army-drafted roadmap announced after Morsi's ousting on July 3 and which provides for new elections in 2014.

Both the interior ministry and the army have repeatedly called on pro-Morsi protesters to lift their sit-ins which have paralysed parts of the capital and increased divisions in the country.

Authorities have promised Morsi loyalists a safe exit and said an end to their protests would allow the Muslim Brotherhood to return to political life.

On Sunday, Sisi met Islamist leaders to try to mediate a solution with Morsi supporters.

He met "several representatives of the Islamist movements... and stressed that there are opportunities for a peaceful solution to the crisis provided all sides reject violence," army spokesman Colonel Ahmed Aly said in a statement.

Among those attending the talks were influential Salafist clerics Sheikh Mohammed Hassan and Mohammed Abdel Salam, who just days ago addressed pro-Morsi supporters at a rally.

"The Islamists who met Sisi, while not members of the Muslim Brotherhood, have been supporting them at the Rabaa al-Adawiya sit-in. Hopefully, the Brotherhood will listen to what they have to say to find a way out of the crisis," a source close to the talks said.

But Yasser Ali, a spokesman for the pro-Morsi demonstrators, said the clerics had met Sisi "without having been mandated".

Burns had also met with members of the Brotherhood's political arm, which later stressed its continued commitment to "legitimacy, which stipulates the return of the president, the constitution and the Shura Council," or upper house of parliament.

The Islamists' declaration suggested Burns had failed to shift their position.

"We affirm our welcome of any political solutions proposed on the basis of constitutional legitimacy and rejection of the coup," said the Freedom and Justice Party statement.

During his visit, the US envoy sat down with Foreign Minister Nabil Fahmy in a bid to broker a compromise as Washington kept up the pressure from afar, with Defence Secretary Chuck Hagel urging Sisi to support an "inclusive political process", the Pentagon said.

The diplomatic push came as the Washington Post published an interview with Sisi in which he urged Washington to pressure Morsi supporters to end their rallies.

"The US administration has a lot (of) leverage and influence with the Muslim Brotherhood and I'd really like the US administration to use this leverage with them to resolve the conflict," he said.

Sisi said that police, not the military, would be charged with dispersing the protests, and insisted that millions of Egyptians "are waiting for me to do something".

But Fahmy insisted authorities have "no desire to use force if there is any other avenue that has not been exhausted".

"There is an open invitation for all political forces to participate. The door is open for everybody, including the Brotherhood, to participate in the process," he told reporters.