Sunni Arabs said on Monday they would rejoin talks to draft a new constitution for Iraq, in the hope of rescuing a political process that has been strained by unrelenting bloodshed.

The Sunnis walked out of the talks last week after one of their committee members was gunned down in Baghdad.

At talks on Monday they secured pledges of better security and a probe into the assassination.

"We will definitely return tomorrow," said Saleh Mutlaq, spokesman for the National Dialogue Council, a Sunni umbrella group to which slain committee member Mijbil Sheikh Esa belonged.

Abdul Nasser Janabi, a committee member from another Sunni group, said his group's demands had also been met. The speaker of parliament announced the compromise in a signed statement.

Efforts to restart work on Iraq's constitution ahead of an Aug. 15 deadline for a finished draft came as attacks killed at least 19 Iraqis and a U.S. soldier.

Secretary of Defense Donald H. Rumsfeld, speaking to reporters on his way to visit Kyrgyzstan, said he expected the constitution to be drafted by the deadline.

"The Sunnis and the Shias and the Kurds are all working very hard on the constitution. They're going to get the job done. They will have a constitution, in my view," he said.

However, Mahmoud Othman, a Kurdish committee member, said that even if the Sunnis rejoined, "I very much doubt at this stage that we are going to have a document ready by the end of this month."

The sides are divided above all on issues of federalism -- how to share power and resources in areas such as the mainly Kurdish north and the Shiite south, where local leaders want autonomy from Baghdad and control of oil wealth.

Fifteen Sunni members were added to the committee last month, joining members drawn from a parliament made up mainly of Shiites and Kurds who were elected in January. Most Sunnis stayed at home during the vote because of a boycott or fear of reprisals.

U.S. Ambassador Zalmay Khalilzad said a constitution was "important in terms of weakening the insurgency . . . winning the population away from al Qaeda and the other foreign terrorists who come here to kill and maim and use Iraqis as cannon fodder for their larger agenda."

[Mutlaq said in an interview Monday with Washington Post special correspondent Omar Fekeiki that the level of violence had "increased with the process of writing the constitution. The issues raised in the process of writing the constitution increased the tension in the security issue," he said. "They didn't decrease it."

["The people started to fear further issues," he said. "When the Iraqis hear that their country would be divided by federalism or connected to Iran by adding Persians as another nation in Iraq, that would make them more eager and insistent to fight, and violence will increase. If the fanatic opinions continued this way, violence will increase."]

Two suicide car bombers struck police checkpoints in Baghdad on Monday, killing at least 15 people, while funerals were held for some of the victims of a truck bombing on Sunday. The U.S. military said 40 people were killed in that attack.

U.S. forces said one soldier was killed by a roadside bomb on Monday in Samarra, a Sunni stronghold north of Baghdad. In Baghdad's Dora neighborhood, four people were killed, including two women, when gunmen stormed their house, police said.

A U.S. government report released on Monday said that insurgents had infiltrated Iraqi security forces. Iraq's police service has accepted recruits with criminal backgrounds and even insurgents planning attacks because of poor vetting procedures, the report said.

Algeria, meanwhile, said on Monday that it had pulled its last diplomatic staff members out of Baghdad following the kidnapping of two of its envoys last week.

Iraqi rescue teams gather at the site of a suicide car bombing at a checkpoint near the Sadeer hotel, once frequented by American contractors. The blast was one of two such attacks in Baghdad that killed 15 people yesterday.