In the latest incident on Saturday, a car bomb exploded outside a public market in New Baghdad killing four and wounding 19.
Two men, a woman and her eight-year-old daughter were killed in the blast in the predominantly Shia neighbourhood, which set off a large fire in the market, police Colonel Hasan Chalub said.
Government spokesman Laith Kubba said Annan met Prime Minister Ibrahim al-Jaafari but provided no additional details.
A UN statement said Annan would meet al-Jaafari, Deputy Prime Minister Rowsh Shaways, former Prime Minister Ayad Allawi, political and community leaders as well as UN staff.
On Friday, al-Jaafari demanded that Syria do more to keep foreign fighters from crossing into western Iraq after a meeting with US Secretary of State Condoleezza Rice. On Thursday he met with British Foreign Secretary Jack Straw.
Rice and Straw said they wanted to encourage participation in parliamentary elections scheduled for 15 December. In addition to meeting with Iraq's Shia leadership, they met with political leaders from the Sunni group.
The leaders of Iraq's predominantly Sunni fighters have called for a boycott of the election.
Condoleezza Rice (L) meets
Prime Minister Ibrahim al-Jaafari
But a Sunni Muslim politician who claims to have contacts with the fighters said on Saturday that some of its members will be running next month's elections and gave their demands and conditions to start peace talks with US forces.
Ayham al-Samarie refused to say how many insurgent groups were planning to have candidates. He did not give further details, and insurgent groups in the past have denied he represents them.
"The resistance should have an active role to help Iraq get out of its crisis," al-Samarie, a former electricity minister, told The Associated Press.
Minutes before al-Samarie spoke, a statement was distributed in his house that allegedly included the fighter's conditions for starting peace talks.
The conditions included an immediate end to all military operations, release of all detainees, the withdrawal of foreign troops from cities and setting a timetable for the full withdrawal of foreign troops from Iraq.