Members of parliament and angry pro-government crowds have called for the swift arrest, trial and execution of Mirhossein Mousavi and Mehdi Karoubi after they staged their first rally in more than a year on Monday in which at least two people died.

But Friday prayers leader Ayatollah Ahmad Jannati, a hard-liner who heads the hugely influential state Guardian Council, said calls to hang them were superfluous as they and their movement were as good as dead already.

“To those who call for their execution, I should say that they have already been executed. They have lost all their credibility and prestige — everything,” he said.

Jannati proposed more restrictions on Mir Hossein Mousavi and Mahdi Karroubi, who are both under house arrest but still managed to organize the largest opposition protest in more than a year on Monday.

“Their communications with people should be completely cut. They should not be able to receive and send messages. Their phone lines and Internet should be cut. They should be prisoners in their homes,” he said.

Mousavi and Karoubi lost the 2009 presidential election to the incumbent Mahmoud Ahmadinejad in a vote they say was rigged, something the government denies.

They became figureheads of the biggest anti-government street protests since the 1979 Islamic Revolution, unrest that was crushed by the end of 2009 by a government which blamed Iran’s foreign enemies for stirring sedition.

Monday’s rallies in Tehran and other cities, inspired by uprisings that toppled the leaders of Tunisia and Egypt, were their attempt to revive a movement that had been all but silent since December 2009.

Another has been called for Sunday to commemorate the deaths of two young men who were shot dead on Monday and authorities say that once again the demonstrations will not be tolerated.

Authorities appeared to be acting to further isolate Mousavi.

An opposition website reported Friday that a new deployment of government guards appeared outside Mousavi’s house and have stopped his three daughters from visiting or contacting their parents since Wednesday. The website, kaleme.com, said the new guards were wearing masks and were closely monitoring people near the house.

The report said the guards belonged to the prosecutor’s office.

Hard-line government supporters have held numerous demonstrations outside Mousavi’s house in past months, and authorities have briefly detained visitors in the past.

The head of Iran’s judiciary, Ayatollah Sadeq Larijani, said Thursday that opposition leaders would be prevented from communicating with their supporters and a possible trial was still on the agenda.

The remarks by these prominent figures, suggest there is still no concrete plan for arresting the opposition leaders, possibly to avoid giving them more public attention.

Late on Thursday, Karroubi’s website, Sahamnews.net, quoted him as saying he was ready to stand trial.

The opposition demonstrations on Monday were aimed at showing solidarity with Egypt’s uprising but turned into a major opposition rally. Two people were killed in clashes with police.

Mousavi and Karroubi are leaders of a protest movement that grew out of the disputed presidential election in 2009 in which Mahmoud Ahmadinejad was re-elected. Both men ran against Ahmadinejad, and Mousavi claims he was the rightful winner but that he was deprived of victory through fraud.

Hundreds of thousands of protesters poured into the streets after the election to protest the alleged fraud.

The opposition says scores were killed in the massive security crackdown.

Dozens of opposition members and activists were sentenced to prison terms from six months to 15 years in the crackdown.