Despite the fresh opening between the government and the militant organizations ¡ª which do not include al-Qaida or Islamic terror groups ¡ª a top Iraqi commander said Baghdad's forces would not be ready to keep the peace for at least a year in Anbar province, the insurgent heartland.

And President Bush brushed aside expectations of a significant U.S. troop drawdown starting in September. He said decisions on troop strength would be made by the new Iraqi government and based upon recommendations from Gen. George W. Casey, the U.S. commander in Iraq.

The latest bombings came as a reminder of just how difficult establishing security can be in many areas of Iraq. Both markets were jammed with shoppers buying dinner provisions as temperatures began to cool after sunset.

The deadliest attack was a bicycle bombing in Baqouba, the Sunni insurgent stronghold 35 miles northeast of Baghdad. The bombing killed at least 25 and wounded 33, according to Dr. Ahmed Fouad, director of the morgue at Baqouba General Hospital.

Minutes earlier, a blast killed at least 15 people and wounded 56 in Hillah, a mainly Shiite city 65 miles south of the capital, said police Capt. Muthana Khalid.

Police reports from across the country listed at least 22 other deaths Monday, victims of sectarian murders or bomb and shooting attacks.

The seven insurgent organizations who approached the government are mostly made up of former members or backers of Saddam Hussein's government, military or security agencies, and were motivated in part by fear of undue Iranian influence in the country, lawmakers said.

If confirmed, their offer would mark an important potential shift and could stand as evidence of a growing divide between Iraq's homegrown Sunni insurgency and the more brutal and ideological fighters of al-Qaida in Iraq, who are believed to be mainly non-Iraqi Islamic militants.

Kurdish lawmaker Mahmoud Othman linked the offer to Prime Minister Nouri al-Maliki's national reconciliation plan, involving amnesty for opposition fighters except those who had killed Iraqis, were involved in terrorism or committed crimes against humanity. Al-Maliki's plan, disclosed Sunday, was thought to have denied amnesty to any insurgent who had killed American forces, though the wording was vague.

The Mujahedeen Shura Council, the terrorist umbrella organization that includes al-Qaida in Iraq, rejected the reconciliation plan.

"The servant of the crusaders, Nouri al-Maliki, has come forward with a new, sinister project aimed at extracting his crusader overlords from their morass," the organization said in an Internet statement.

Shiite lawmaker Hassan al-Suneid, who first reported insurgent groups' gesture, said al-Maliki was considering a possible meeting with their leaders or contacts through intermediaries. Al-Suneid is a member of the political bureau of al-Maliki's Dawa Party.

The opening was confirmed by Othman, a close associate of President Jalal Talabani, who held face-to-face talks with seven insurgent organizations about two months ago. It was never clear which groups Talabani met with.

Al-Suneid gave the names of six of the seven organizations that approached the government Monday: the 1920 Revolution Brigades, the Mohammed Army, Abtal al-Iraq (Heroes of Iraq), the 9th of April Group, al- Fatah Brigades and the Brigades of the General Command of the Armed Forces.

"I expect that those groups are the same ones that have made contacts with President Talabani, and now they are widening the range of their contacts. Now they are more serious after the announcement of the (reconciliation) plan," al-Suneid told the AP.

Othman was unable to name the groups or say whether they were the same ones Talibani had contacted. But he said they also sought talks with U.S. forces.

"They want negotiation with the Americans. The seven groups have real fears of the Iranian influence. They think that the Americans will eventually leave, but Iran is a neighbor and is not going anywhere," he said.

Many Arabs agree with the U.S. government that Iran, a majority Shiite Muslim country run by a fundamentalist theocracy, has undue influence in Iraq, also a majority Shiite nation. Many Iraqi Shiites ¡ª including current religious and political leaders ¡ª spent years in exile in Iran.

One of the seven groups, the 1920 Revolution Brigades, operates primarily in Anbar province. The organization claims it has conducted operations only against U.S. forces. They and other insurgents were said to have protected polling places in Anbar province during December parliamentary voting.

Another group, the Mohammed Army, is made up of former members of Saddam's Baath party, members of his elite Republican Guards and former military commanders. It, too, has focused attacks on the U.S. military and played a role in the November 2004 battle for Fallujah.

"The groups have said they are ready to lay down their arms, but they have some conditions. The al-Maliki initiative could help them to enter the political process," Othman said. He would not detail the insurgents' conditions.

A meaningful truce with insurgents would make it much easier for the United States to withdraw troops from Iraq.

Regardless of insurgents' plans, Brig. Gen. Jaleel Khalf estimated it would take a year for the Iraqi army assume control of Anbar province. And he called that estimate "optimistic under the best of circumstances."

Khalf's timeframe closely aligns with forecasts from the U.S. military.

"I don't think by this winter we'll be quite ready to turn over completely" to Iraqi forces, Army Col. Sean MacFarland said recently. He commands the 1st Brigade Combat Team, 1st Armored Division that oversees Ramadi. Ramadi, with a population of 400,000, is Iraq's largest Sunni city.

Khalf said the Iraqi army would need about 15,000 soldiers to control the vast province that spreads like a fan from Baghdad to the Saudi Arabian, Jordanian and Syrian borders. The Iraqi Defense Ministry says it now has about 12,000 soldiers in Anbar.

"If our forces are built on a proper foundation and equipped with modern weapons and materials such as heavy artillery, mortars, and new light weapons that are held by the world's modern armies, we could take over security in Anbar in about a year," he said.

Iraqi military preparedness has come under intense focus in recent days after reports that Casey had developed a withdrawal plan that could see American troop strength reduced by two brigades in September. The plan was said to include cutting total American forces, now at about 127,000, by about half at the end of 2007.