The United States on Wednesday urged the Egyptian military and the country's bitterly divided political factions to resolve their differences through dialogue and agree a return to democratic rule.

"Over the course of the last several days, envoys of the United States, the EU, the UAE and Qatar provided constructive ideas to the Egyptians in order to help prevent further violence and help advance the transition to a democratically elected civilian government," said State Department spokeswoman Jen Psaki.

Egypt's military on Wednesday said it had killed 60 "terrorists" in Sinai in the month after Mohammed Morsi's ouster on July 3, which fueled militant attacks in the restive peninsula.

The military "killed 60 individuals", according to a bullet-point video it released, titled "Losses of terrorist elements in exchanges of fire with security forces".

Western and Arab efforts to mediate an end to Egypt's political deadlock have failed, the presidency said Wednesday, signalling a possible crackdown on Islamists that has sparked fears of more carnage.

The statement came hours after U.S. Deputy Secretary of State William Burns left Cairo, having made no headway in finding a compromise between the army-installed government and supporters of deposed Islamist president Mohammed Morsi.

Gunmen in Egypt's restive Sinai Peninsula gunned down a politician known for his support of the military on Wednesday, security official and medics said.

The Bedouin politician's influential tribe immediately blamed Islamist militants who have conducted daily attacks on security forces since the military overthrew Egypt's Islamist president Mohammed Morsi on July 3.

By Giza's Great Pyramids, souvenir vendors wait restlessly in the shade, watching for the handful of tourists who still make their way down the empty street to the once-bustling landmark.

The 2011 revolution that toppled dictator Hosni Mubarak dealt a severe blow to the country's tourist industry, once a mainstay of Egypt's economy.

U.N. Secretary General Ban Ki-moon appealed anew Tuesday for the release of deposed Egyptian president Mohammed Morsi, in a telephone call with Egypt's foreign minister.

"He called for an end to all violence and urged the interim authorities to ensure protection of the fundamental human rights of all Egyptians, including freedom of speech and assembly," a U.N. statement said, referring to Ban's message to Egyptian Foreign Minister Nabil Fahy.

An Egyptian soldier was shot dead and two others were wounded in two separate attacks in the Sinai Peninsula on Monday, security officials said.

Gunmen shot at an army checkpoint outside a military building in the north Sinai town of El-Arish, killing one soldier.

Veteran Middle East diplomat Robert Ford is Secretary of State John Kerry's choice to be the next U.S. ambassador to Egypt, the New York Times reported Monday.

Ford is best known for actively challenging Syrian President Bashar Assad and meeting with protesters when he was the U.S. ambassador in Damascus 2011-2012. He was withdrawn when security markedly deteriorated in the war-torn country.

An Egyptian court on Sunday set a trial date for Muslim Brotherhood leaders in a move likely to enrage supporters of ousted Islamist president Mohammed Morsi.

It came as U.S. Deputy Secretary of State William Burns met the army chief amid intense efforts to try to resolve the political crisis since the army ousted Morsi in a July 3 coup.

Egyptian authorities on Sunday banned Yemeni rights activist and Nobel Peace Prize winner Tawakkol Karman from entering the country for "security reasons," airport officials told Agence France Presse.

Karman was held at Cairo airport on arrival and ordered to return on the flight back to Yemen, the officials said without providing further details.