Al-Samarra'i, a former electricity minister, said on 7 June that the two groups -- the Mujahedin Army and Islamic Army of Iraq -- are ready to disarm and begin talks with the government.
Al-Samarra'i said he began contacting the groups' political leaders five months ago. The disclosure appears consistent with comments from a senior Shi'ite legislator, Humam Hammudi, who recently said the government had opened indirect channels of communication with some insurgent groups.
Yahia Said, a researcher on Iraq and other transitional nations at the London School of Economics, says some insurgent groups have long indicated they are ready to negotiate.
"There were groups who were indicating willingness to negotiate for a quite long time now. And these other groups who wanted to distance themselves from all the suicide bombings and attacks on Iraqi civilian targets. That said, I think the operation in the west of the country must have had an impact also on some of these groups who are willing to negotiate," Said says.
The two groups are believed to represent more than half of the total insurgent forces. The Mujahedin Army has claimed responsibility for scores of attacks, including the April downing of a helicopter carrying 11 civilians, and the kidnapping of Indonesian journalists who were released unharmed in February.
The Islamic Army in Iraq is a significant insurgent group that has claimed responsibility for attacks on U.S. and Iraqi forces as recently as in the last two weeks.
However, Said says a possible truce is unlikely to stop suicide bombers attacking civilians. These attacks are usually carried out by radical groups, such as the one led by Abu Mus'ab al-Zarqawi, the Jordanian-born militant considered Al-Qaeda's leader in Iraq.
Said says it is difficult to say if recent military operations are pushing insurgents to the negotiating table. He also says it is too early to say if the current military operations are a success.
"The military action is necessary although I think these attacks have been too broad. I think they have reported that hundreds of people have been arrested. I have serious doubts that all these people are guilty. I think many innocent people have been caught," Said says.
Jeremy Binnie, a Middle East analyst with "Jane's Sentinel" in London, says it is too early to say if the negotiations with insurgents will take place at all.
He is also cautious about the ongoing military crackdown. Reports say the major offensive in Tal Afar -- near the border with Syria -- includes helicopters, tanks, and armored military vehicles.
"We've already seen in Al-Fallujah, that a success there didn't really stem an insurgency a great deal. They [insurgents] already proved their adaptability. As we looked to Al-Fallujah, there was a sort of analysis -- that this was going to be a turning point, but it wasn't. They moved elsewhere; they adapted to the situation," Binnie says.
Meanwhile, insurgents are striking back. Bombings yesterday killed at least 33 civilians and three American soldiers in northern Iraq.
Said says he is concerned that there are no strong efforts to integrate Sunnis into the political process.
"When you have predominantly Shi'a troops operating in Sunni areas, then you always have the risk of exacerbating ethnic tensions. So these operations generally are very blunt tools for the desired objective," Said says.
The influential Sunni Muslim Clerics Association said the operation, which has led to nearly 900 arrests, could spark sectarian strife as mostly Sunnis are being targeted.
Today, Iraqi Sunni Arabs said they would demand a greater role in drafting the country's new constitution.
Adnan al-Dulaymi, presiding over a meeting of more than 150 Sunni Arab leaders in Baghdad, said they want at least 25 representatives named to a parliamentary committee drafting the constitution.
The 55-member committee said on 5 June it had 13 places for unelected Sunnis, who are underrepresented in parliament, having largely boycotted January's elections.