Sunni Muslims say they will rejoin the negotiations on a new constitution for Iraq.
They hope to rescue the political process, which has been severely strained by a series of attacks and bombings in recent weeks.
The Sunnis walked out of the talks last week after one of their committee members was shot dead near a restaurant.
At crisis talks today, they secured pledges of better security and a probe into the assassination.
15 Sunni members were drafted on to the committee last month, joining members drawn from a parliament mainly made up of Shi'ites and Kurds elected in January when most Sunnis abstained because of a boycott or fear of reprisals.
Two suicide car bombers struck police checkpoints in Baghdad this morning, killing at least 15 people, while funerals were held for some of the 25 victims of yesterday's truck bomb.
At dawn a suicide bomber blew up a minivan packed with explosives at a checkpoint near the Sadir hotel in the city centre.
A second bomber struck Ansour Square, near an entrance to the fortified Green Zone government and diplomatic compound.
Negotiations over the constitution are far from over. A draft is due by mid-August, but 1 August is the deadline for announcing a 6-month extension if the committee decides it needs more time.
Washington says an extension would deprive the political process of momentum.
