The wife of Egypt's deposed President Mohamed Morsi has addressed thousands of his supporters at a protest rally in Cairo, in her first appearance since her husband's overthrow.

Naglaa Mahmoud, Morsi's rarely seen wife, made a surprise appearance on stage at the main demonstration in the capital on Thursday, as Morsi supporters celebrated Eid al-Fitr at a site which has been used regularly for protests in Nasr City.

Mahmoud appealed for her husband's return as the crowds roared, "Returning! Returning!"

"He is coming back, God willing," she said during her first appearance since the July 3 military coup.

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Earlier, the US and the European Union called on all sides in Egypt's political crisis to end the "dangerous stalemate" after the interim government said foreign mediation efforts had failed.

The joint statement came as the army-installed government repeated its threat to take action against Morsi supporters.

Egypt's rival political camps held mass rallies in Cairo to celebrate and hold prayers for the Muslim festival of Eid.

Morsi's children joined their mother at the Nasr City protest camp and called for release of their father.

Morsi's location

The Egyptian press initially suggested that Mahmoud was held with her husband in undisclosed location along with one of her children.

She did not say during the rally where she had been since the coup.

Morsi is being held with his top aides, several of whom have been transferred over the past days to a prison in southern Cairo.

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They face charges including instigating violence in various incidents that led to deadly street violence over one-year-rule of Morsi.

Interim President Adly Mansour, in a message on the eve of the Eid al-Fitr holiday, said Egypt was in critical circumstances.

The interim government would press on with its own plan to hold new elections in nine months, he said.

"The train of the future has departed, and everyone must realise the moment and catch up with it, and whoever fails to realise this moment must take responsibility for their decision," he said.

US envoy William Burns headed home after days of trying to broker a compromise between the government and Morsi's Muslim Brotherhood. European Union envoy Bernardino Leon stayed on in the capital in the hope of reviving the effort.

Western concern

The EU and the US said they were very concerned that the Egyptian parties had not found a way to break what they called "a dangerous stalemate".

However, a person involved in the mediation effort told Reuters news agency that the authorities and Morsi's Muslim Brotherhood might yet step back from confrontation and implement mutual confidence building steps that could lead to a negotiated settlement.

Government and military sources said the talks were not terminated but had been frozen to assuage public anger over perceived foreign interference in Egypt's affairs and among some at the authorities' willingness to negotiate with the Brotherhood after months of demonising them.

A military source said the authorities were holding back from using force to clear the pro-Morsi protest camps partly due to fear that Vice President Mohamed ElBaradei, a liberal, would resign, removing a source of political legitimacy for army rule.

Source: Al Jazeera and agencies