The two spoke to Aljazeera on Sunday live from Baghdad.
Ibrahim al-Shammari, spokesman for the al-Jaish al-Islami (Islamic Army), said that the proposal by Nuri al-Maliki, the prime minister, is far from being an "initiative for national reconciliation".
"If the proposal excludes those who fought the Americans, then who is supposed to be meant by this proposal?" al-Shammari said.
"We do not recognise this government. ... We do not mind a technocrat government that carries out the day-to-day interests of Iraqi people."
In an effort to leave the the door open for future dialogue, al-Shammari said talks would have to be with the Americans.
"How can they ask us to disarm and to attend negotiations with a government appointed by the occupation?
"If the Americans are serious, we are ready to have negotiations with them as counterparts and on the basis of equality. Moreover, it is not possible to sit with their agents," he said.
Muhammad Hasan al-Gailani, spokesman for Thwrat al-Ishreen Brigades (Brigades of 1920 revolution) said that the current Iraqi politicians are not the right party to launch a reconciliation initiative.
"The problem is not between the Iraqi resistance and al-Maliki's people, our problem is with the US occupation forces. Why should we deal with al-Maliki's proposals?" al-Gailani said.
"The resistance has a strict stance to resist the occupation and all squads of resistance have rejected the initiative because this initiative didn't talk about the occupation. We have never heard of those names of resistance groups that are said to have agreed on the plan," he said.
Baghdad's oldest district, Adhamiya, witnessed a new round of fighting between its elite residents and US and Iraqi forces.
Mortar fire and gunfire rang across the eastern Baghdadi neighbourhood. Fighters armed with rocket-propelled grenades prowled the streets, a Reuters witness said. US armoured vehicles entered the area as US helicopters flew overhead.
Saturday's bomb in Baghdad's poor
al-Sadr City neighborhood killed 62
It was not immediately clear who was involved in the clashes in Adhamiya, and the US military declined comment on "current operations".
Adhamiya was the last Baghdad neighbourhood to fall to US forces in 2003, after a three-day-battle that left many dead from both sides.
A day after the kidnapping of one of its MPs, the Iraqi Accordance Front, the main Sunni Arab political bloc, decided to boycott parliament until its member is released.
Tayseer al-Mashahadani was kidnapped by gunmen who seized her in a mainly Shia district of Baghdad.
Violence in the capital
In more violence that has defied a massive government clampdown in the capital, a car bomb killed two people and wounded 13 outside a popular restaurant in central Baghdad.
A car bomb exploded in Baghdad's Huriya district, wounding 13 people, an Interior Ministry source said. The target of the bomb was not clear.
A civilian was killed and three people were wounded, including a police officer, when a car bomb exploded near a police patrol in central Baghdad, the Interior Ministry said.
Four civilians, including an elderly woman and a boy, were wounded on Saturday in the town of Khaffajiya, near Haditha, when US troops fired mortar rounds "at a known historical site from which anti-Iraqi forces had previously launched attacks", the US military said in a statement.
Three people were killed and 21 wounded in Mahmudiya, 25km southwest of Baghdad, when a car bomb exploded in a market, police and hospital officials said.
In Buhruz, the village just south of Baquba in which Abu Musab al-Zarqawi was killed, an Iraqi soldier was wounded when a roadside bomb went off near his patrol, police said.