* Opposition says call to topple regime didn't mean Mursi
* Two more protesters die of wounds, death toll 59
* President's office says to probe beatings
By Paul Taylor
CAIRO, Feb 4 (Reuters) - Egypt's main opposition alliance has got itself into a muddle by appearing to endorse a call for the overthrow of Islamist President Mohamed Mursi, then backing away.
"The NSF will fully align to the demands of the Egyptian people calling to topple the regime of tyranny and domination of the Muslim Brotherhood," a statement by the National Salvation Front issued late on Saturday said.
After a week of violence between protesters and the security forces in which 59 people have died, it called for Mursi, his interior minister and "all his partners in those crimes" to be investigated and put on trial for "killings, torture and illegal detentions".
"The NSF supports all forms of peaceful protest to achieve these demands, and calls for the Egyptians to rally peacefully in all the streets of Egypt in defense of Egyptian dignity."
The Front includes liberal politicians such as former U.N. nuclear watchdog Mohamed ElBaradei and former Arab League chief Amr Moussa, who last week signed a statement mediated by the country's leading Muslim scholar renouncing violence and calling for a national dialogue.
However, the NSF's spokesman, Khaled Daoud, said on Monday the coalition of liberal, social democratic and leftist parties was not demanding the removal of Egypt's first democratically elected president just seven months after he took office.
"We are not calling for the overthrow of President Mohamed Mursi right now. We believe he is elected but that doesn't give him the right to change all the rules of the game," Daoud told Reuters.
Ahmed Kamal, a spokesman for Moussa's Congress Party, said the wording had been chosen carefully to warn against "any violent practices and new dictatorship" without questioning Mursi's democratic legitimacy.
The NSF said it would not engage in dialogue until what it called the bloodbath had stopped, those responsible were tried, and the opposition's previously stated demands were met.
Those demands include forming a national unity government, which Mursi has rejected before parliamentary elections due in April, and revising a controversial Islamist-leaning constitution adopted last December.
The statement was issued in reaction to an incident that sparked public outrage in which police were caught on video beating and dragging a naked man during a protest on Friday.
The man, Hamada Saber, 48, was shown on state television in a police hospital saying protesters had stripped him. He later reversed his statement and told a public prosecutor that riot police were responsible for the attack.
Another activist picked up by police in Cairo's central Tahrir Square on Jan. 25 and later taken unconscious to a hospital died of his wounds on Monday, prompting fresh accusations of police brutality by human rights groups.
Mohamed el-Gendi, 23, was a member of the Popular Current party. Doctors at Hilal hospital said Gendi was in a coma when he died and had suffered brain damage and multiple fractures.
The president's office said it was investigating the causes of Gendi's death as well as the televised incident involving Saber, and insisted there would be no return to the violations of human rights that prevailed before the 2011 uprising that toppled former President Hosni Mubarak.
Opposition critics say little has changed, the interior ministry remains unreformed and the police have not been purged.
A brief clash erupted on Monday when young mourners carrying the body of one of latest two protesters to die of wounds threw stones and metal objects at riot police guarding the British Embassy, near Tahrir Square, site of a permanent protest encampment. The police fired tear gas to disperse them.
The hardline Islamist Nour Party accused the opposition of stoking youth violence for political gain to try to oust the president.
A statement on the Salafist Nour Party website condemned what it called unrealistic demands "such as overthrowing the legitimate president or calling for early presidential elections or calling for amendments to the constitution far removed from the correct way as stated in the constitution".
An opposition official, speaking on condition of anonymity, said the NSF leadership was trying to give political voice to the anger of the street protesters rather than goading them on. (Additional reporting by Marwa Awad and Tom Perry; Writing by Paul Taylor; Editing by Robin Pomeroy)