They are demanding that the Iraqi government and Washington set the timetable.
Eight of the eleven groups that have approached Nuri al-Maliki's government have banded together under the umbrella of The 1920 Revolution Brigade.
All 11, however, have issued identical demands, said the groups' representatives and government officials.
They spoke on condition of anonymity because of the sensitivity of the information and for fear of retribution.
The groups do not include the powerful Islamic Army in Iraq, Muhammad Army and the Mujahidin Shura Council, an umbrella for eight groups including al-Qaeda in Iraq.
Most of the 11 groups operate north and north-east of Baghdad in increasingly violent Salahuddin and Diyala provinces.
The total number of anti-US fighters is not known, nor is it known how many men belong to each group.
But there are believed to be about two dozen organisations, meaning the 11 that are in contact with the government represent nearly half of the known groups.
A key Sunni politician, however, predicted a big majority of anti-US fighters could be enticed to the negotiation table.
"If the reconciliation initiative is implemented properly, 70% of the insurgent groups will respond positively," said Naseer al-Ani, an official with the largest Sunni political group, the Iraqi Islamic Party of Tariq al-Hashimi, an Iraqi deputy president.
Al-Maliki, the Iraqi prime minister, in remarks broadcast on national television on Wednesday, did not issue an outright rejection of the timetable demand but said it was unrealistic because he could not be certain when the Iraqi army and police would be strong enough to assume full responsibility for the country's security.
Al-Hashimi says anti-US fighters
could be enticed to negotiate
The administration of George W Bush has forecast that US soldiers would be needed in Iraq for years to come, although American military officials are said to be considering plans for significant reductions - as much as half the current force of 127,000 - by the end of next year.
There have been sporadic contacts between fighters and the Iraqi government in the past, but the openings have intensified after al-Maliki issued his plan for national reconciliation on Sunday.
He said he wanted to pardon detainees who have not committed terrorist acts or killings.
In addition, al-Maliki has proposed an amnesty for anti-US fighters still in the field. He ruled out including opposition fighters who have killed multinational force soldiers or Iraqis.
Amnesty proposals, however, have always offered opposing sides a means to negotiate because determining who is eligible leaves considerable room for manoeuvre.
The issue is extremely sensitive in the US, which has lost hundreds of men and women to attacks by these fighters.
But proving that anti-US fighters who remain at large have conducted fatal attacks against Americans would, in many - if not most - cases, be a very difficult task.
In any case, violence continues to take a bloody toll.
On Wednesday, a car bomber blew up himself near a Sunni mosque in a market south of Baquba, killing one person and wounding 12.
In western Baghdad, a roadside bomb targeting a US convoy exploded, killing an Iraqi civilian and wounding another.
Separately, armed men killed the customs director for central Iraq and his driver in a predominantly Sunni neighbourhood in Baghdad.
Coinciding with the flurry of contacts between fighters' representatives and the Iraqi government, Zalmay Khalilzad, the US ambassador, held talks on Tuesday with Saudi King Abdullah.
The Saudis have vast influence with many Iraqi Sunni fighters, and it was widely believed Khalilzad was seeking Saudi intervention to promote further movement towards reconciliation.
The contacts between the Iraqi government and anti-government fighters also coincide with a growing disagreement inside the ruling Shia establishment here.
Al-Maliki is said to be increasingly disenchanted with the close ties between country's most-powerful Shia organisation and Iran.
Al-Maliki, of the Dawa Party, and Abdul Aziz al-Hakim, leader of the Supreme Council for the Islamic Revolution in Iraq, which has deep historic ties to the Iranians, reportedly are at odds over the future of Tehran's influence in Iraq.
Al-Maliki's reported concern with Iranian intervention in Iraq meshes with fears of the Sunni fighters, whose representatives have made no secret that those concerns partly motivate their interest in reaching an accord with the al-Maliki government.
Many of Iraq's current and most powerful Shia politicians and religious figures spent years in Iranian exile under Saddam. Iran is ruled by a theocracy.
In addition to the withdrawal timetable, the anti-US fighters have demanded:
Al-Maliki's (R) amnesty proposal
is extremely sensitive for the US
- An end to US and Iraqi military operations against anti-US forces.
- Compensation for Iraqis killed by US and government forces and reimbursement for property damage.
- An end to the ban on army officers from Saddam Hussein's government in the new Iraqi military.
- An end to the government's ban on former members of the Baath Party - which ruled the country under Saddam.
-The release of anti-US fighters in detention.
- Recognition of anti-US groups as legitimate resistance organisations.
The groups have also demanded that the Arab League, Saudi Arabia and the Association of Muslim Scholars serve as observers of any face-to-face talks with the government. The influential Muslim scholars' group was formed after Saddam's ouster to run Sunni religious affairs in the country.
The 1920 Revolution Brigades, which is serving as the umbrellas structure for eight of the groups, was established in the Sunni Triangle shortly after the 2003 US-led invasion and has claimed responsibility for attacking American troops, including the downing of two helicopters in 2004.
Its name refers to Iraq's historical fight against British colonialism.
"If they set a two-year timetable for the withdrawal we will stop all our operations immediately," said the group's leader in a brief telephone interview with The AP.
The man, who refused to give his name for security reasons, spoke from the telephone of one of the mediators. Others present issued similar remarks.
Besides the 1920 Revolution Brigades, the group of eight includes Abtal al-Iraq (Heroes of Iraq), the 9th of April Group, al-Fateh Brigades, al-Mukhtar Brigades, Salahuddin Brigades, Mujahidin Army and the Brigades of the General Command of the Armed Forces.
The three other groups are small organisations that also mainly operate in areas north of Baghdad.