CAIRO (Reuters) - International envoys trying to end Egypt's political crisis are urging the Muslim Brotherhood to "swallow the reality" that Mohamed Mursi's time as president is over but the group is refusing, the Brotherhood's spokesman said on Monday.

Gehad El-Haddad also confirmed that the envoys had visited jailed deputy Brotherhood leader Khairat El-Shater in prison in the early hours of Monday, but he had cut the meeting short, saying they should be talking to Mursi.

Speaking about talks with the envoys in recent days, Haddad said the Brotherhood faced pressure to "accept that the military coup has happened and try to recover with minimum damage".

He was referring to Mursi's July 3 removal by the army following mass protests against his rule.

"We refuse to do so," Haddad said, adding there was no agreement on how to start talks.

Diplomats from the United States, European Union, United Arab Emirates and Qatar are all in Cairo in a bid to mediate an end to the crisis set off by Mursi's overthrow.

The state news agency MENA earlier said diplomats including U.S. Deputy Secretary of State William Burns and European Union envoy Bernardino Leon had met Shater after midnight at Tora prison south of Cairo.

Shater told them he could not speak on anyone's behalf, that Mursi was the only person who could "solve the mess" and that the only solution was "full restoration of constitutional legitimacy and reversal of the coup", Haddad said.

"They invited him for discussions but he ended it abruptly saying 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 via a fellow Brotherhood detainee who had been allowed a family visit.

While the account appeared at odds with reports that Shater had spent an hour with the envoys, elements of it tallied with a report in the privately owned Al Masry Al Youm newspaper.

The paper's website quoted a senior security official as saying Shater told the envoys he would only hold talks with them in the presence of Mursi because he was "the legitimate president".

Haddad said: "We still insist that the ground has to be the constitutional legitimacy of the state, and working towards restoring it.

"The envoys still carry the position that we should swallow the reality, and accept that the military coup has happened and try to recover with minimum damage, and we refuse to do so."

(Writing by Tom Perry; Editing by Michael Georgy and Paul Taylor)