Iranian authorities have blamed the two leaders, Mir Hossein Mousavi and Mehdi Karroubi, for violence on Monday after they called for a rally which turned into deadly anti-government protests in which two people were killed and several were wounded.
Furious lawmakers and a leading cleric on Tuesday accused them of being behind the violence and said they should be hanged.
Karroubi, once a pillar of the regime, said in a statement posted on his website Sahamnews.org, he was ready to "pay any price."
"I declare that I am not afraid of any kind of threat and as a soldier of this great nation for the past almost 50 years, I am ready to pay any price," he said.
"I am warning that before it is too late, take out the buds from your ears and listen to the voice of the people. Forcing violence and opposing peoples' wishes will last only for a certain time," the cleric said.
He added that Iran's rulers must take "lessons from the destiny of those governments who distanced themselves from the people."
In a separate statement on his own website Kaleme.com, Mousavi criticised the authorities and praised the protesters for turning out in Monday's rally.
"The glorious rally on 25th Bahman (February 14) is a great achievement for the great people of a great nation and for the Green Movement," Mousavi said, referring to the opposition movement and its supporters who took to streets on Monday.
Mousavi distanced his movement from "foreigners" whom Iran's conservative lawmakers say are influencing it.
"This great movement is being attacked from two sides, by authoritarians who are eyeing future posts and foreigners who are seeking their own interest," said Mousavi, who was the main rival to President Mahmoud Ahmadinejad during the 2009 presidential election.
"Both tried to relate the movement to Zionism and America... The Green Movement has always maintained distance from foreigners and its goal is to resurrect the values of the (1979) revolution and of late Imam (Khomeini.)"
In Monday's protests, two people were killed and several were wounded, including nine members of security forces, officials say, as riot-police fired tear gas and paintballs at demonstrators.
The latest unrest triggered fury in Iran's conservative-dominated parliament, with lawmakers demanding that Mousavi and Karroubi be executed.
"Mousavi and Karroubi should be executed! Death to Mousavi, Karroubi and Khatami!" lawmakers shouted in the house Tuesday, state news agency IRNA reported.
They said the United States, Britain and Israel had orchestrated the protests through the opposition leaders, who, according to parliament speaker Ali Larijani, were being "misled" by Iran's arch-foes.
Ayatollah Ahmad Khatami, a hardline cleric who often leads Friday prayers in Tehran, applauded the MPs and accused Mousavi and Karroubi of being "mohareb," or enemies of God, adding that they deserved the harshest of punishment.