Tuesday's announcement came as the Shiite-dominated parliament reached out to Iraq's disgruntled Sunni Arab minority by offering a role on the committee drafting a new constitution.
But in a development that could affect efforts to get Shiites and Sunnis working together, President Jalal Talabani said Saddam, a Sunni, could be put on trial in the next two months. The former dictator's lawyers said they knew nothing about that.
Foreign extremists are thought to be a small portion of the Sunni-dominated insurgency, although they are blamed for some of the worst bombings and other bloodshed that have killed 765 Iraqis in the month since the new government took power.
Officials said the body of Anbar Gov. Raja Nawaf Farhan al-Mahalawi was found Sunday after troops engaged in a fierce firefight with foreigners holed up in a house in Rawah, a desert village 175 miles northwest of Baghdad.
In other recent developments:
The Baghdad crackdown, Operation Lightning, involves more than 40,000 soldiers. "We have so far achieved good results and rounded up a large number of saboteurs. Some are Iraqis and some are non-Iraqis," al-Jaafari said, but provided no details.
The battle after which soldiers found the body of the Anbar Province governor killed two Syrians, an Algerian and a Jordanian and wounded two Saudis and a Moroccan, a U.S. military spokesman, Maj. Wes Hayes, said.
"After questioning the wounded foreign fighters, coalition forces investigated the house and discovered (al-Mahalawi's) body, which had not been shot," Hayes said. An Iraqi government spokesman, Laith Kuba, said the governor apparently was killed by falling rubble. He was chained to a tank of propane.
Al-Mahalawi was kidnapped May 10 during an offensive by U.S. Marines to clear foreign fighters from a stretch of desert along the border with Syria. His fate had been shrouded in mystery since an announcement by relatives and a government official that he had been released two weeks ago.
In an effort to calm sectarian tensions worsened by the relentless insurgency, key lawmakers said Tuesday they wanted 13 Sunni Arabs to join a 55-member committee of legislators given the task of drafting Iraq's constitution by mid-August.
The 13 Sunnis would not have a right to vote, because they were not elected to the 275-member National Assembly, but legislators sought to ease any concerns by offering assurances the panel would make decisions only by consensus.
Although Sunni Arabs make up 15 percent to 20 percent of Iraq's 26 million people, there are just 17 Sunni Arabs in parliament, because most did not take part in the historic Jan. 30 election.
Even though Shiite Arabs and Kurds form a strong overall majority, Sunni Arab support is needed for the constitution because a negative vote in three of Iraq's 18 provinces during a national referendum would block the charter and Sunni Arabs have big majorities in four of them.
The influential Association of Muslim Scholars, one of the Sunni groups whose support was sought for the committee, said it was "unacceptable" for the 13 not to be able to vote. A spokesman, Abdul-Salam al-Kobeisi, said that would only fuel tensions.
Another group, the Iraqi Islamic Party, said it would wait until a Thursday meeting with committee leaders before making a decision.
Committee member Khalid al-Atiyah said the 13 should represent provinces where Sunni Arabs have a majority, while chairman Hummam Hammoudi said they would also include tribal and other leaders.
A comment by Talabani, a Kurd, that Saddam could be tried in two months might upset the delicate balance needed for the constitutional process to succeed.
Talabani told CNN that Saddam committed crimes against the Kurds and others and "the Iraqi people from now are starting to ask for executing Saddam Hussein."
Asked when the trial would begin, he said, "Within two months, I think."
His comments were greeted with surprise from Saddam's lawyers. "I was not informed officially that they are speeding up the trial, but anyway I will check," attorney Khalil al-Dulaimi said.
Saddam has been charged with crimes against humanity. He has been held at a special U.S.-run facility near Baghdad airport since American soldiers captured him in December 2003.