Press reports said on Monday the Association of Religious Combatants issued the threat after a meeting of the party on Sunday, attended by both the president and the speaker of the Majlis or parliament Mahdi Karubi.
Meanwhile, Iran's hardline Guardian Council insisted on Sunday it had no interest in trying to influence the result of parliamentary elections and was reviewing the cases of hundreds of candidates it barred from standing.
At a rare news conference, a spokesman for the Guardian Council moved to play down the crisis sparked by its decision to veto nearly half of the 8200 candidates hoping to stand in next month's vote.
Reformist allies of President Muhammad Khatami have accused the Guardian Council of seeking to ensure an easy win for conservative candidates in the 20 February parliamentary vote.
"For the council, it makes no difference who enters parliament," Guardian Council spokesman Ibrahim Azizi told reporters, including members of the foreign media usually not invited to such press conferences.
Azizi insisted the Guardian Council - one of a number of powerful unelected bodies controlled by hardliners in Iran -
would "not succumb to any pressure or propaganda".
But he said the council would follow the request of Iran's Supreme Leader Ayat Allah Ali Khamenei, who last week moved to defuse the political standoff by urging the Guardian Council to review the cases of those who had been disqualified.
"For the council, it makes no difference who enters parliament"
Guardian Council spokesman
The mass vetting has prompted resignation threats by some government ministers and state governors, a week-long sit-in by dozens of MPs at parliament, and a warning by the reformist run Interior Ministry that it may refuse to run the election at all.
Most of those barred are reformists, including about 80 current MPs.
Reformists secured a comfortable majority of parliament's 290 seats in the last elections in 2000.
"We started to review the disqualifications two days ago and the council will make a decision after going through the documents and proofs," Azizi said.
According to a previously announced timetable, the Guardian Council has until the end of January to decide the fate of those who have appealed against the move to bar them from running.
Those still disqualified have another chance to appeal before campaigning starts on 12 February.
Political analysts believe hardliners and reformists will eventually agree on a smaller number of disqualified candidates so that the election can go ahead.
"The sit-in will continue as long as there is even one unfair disqualification"
But Muhsin Armin, one of the most outspoken reformist lawmakers, said protesting MPs were in no mood to compromise.
"The sit-in will continue as long as there is even one unfair disqualification," he was quoted as saying by the official IRNA news agency on Sunday.
Reformist allies of Khatami have written to the president, urging him to force the Guardian Council to produce a final list of eligible candidates by 22 January.
MPs said they feared the Guardian Council might drag out its review process, leaving reformists too little time to organise an effective election campaign.