The United States' senior military officer has said he will probably recommend withdrawing more US troops from Iraq if security there improves.

The statement by Admiral Michael Mullen, chairman of the Joint Chiefs of Staff, came as the last of the 20,000 soldiers from the so-called surge last year officially ended their tour.

Mullen's comments also came as Iraqi forces took over security control of Diwaniyah province from US troops. Diwaniyah is the 10th of Iraq's 18 provinces to fall under the control of Iraqi forces.

Officials said the remaining eight provinces could be under Iraqi control by December.

US officials say the level of violence across the country is down to a four-year low based on reports of US and Iraqi military deaths, attacks on Iraqi civilians and sectarian violence.

'Unquestionably better'

Mullen said more progress had been made in Iraq than he expected, although he said it had not reached "a tipping point" and was not "irreversible".

"But security is unquestionably and remarkably better," he said following a recent visit to Iraq.

"Indeed, if these trends continue I expect to be able early this fall to recommend to the secretary [of defence] and the president further troop reductions."

Violence continued in Iraq on Wednesday, however, with a car bombing at a popular market in the country's north, police said, killing at least 15 people, including seven children.

Nearly 100 people were injured in the explosion near the town of Tal Afar, 420km northwest of Baghdad, police said.

The attack came a day after bombings killed about 40 people and wounded scores in northern Iraq.

Assessment period

The end of the so-called surge of US troops also marks the start of a 45-day evaluation period to assess the security situation in Iraq and determine how many more soldiers could be pulled out.

In recent months US military commanders have pointed to significant improvements in Iraq, including reduced violence and the growing capacity of Iraqi forces.

US officials have been hoping that if security improves, they may be able to send more units to Afghanistan, where they say violence is increasing.

Robert Gates, the US defence secretary, said on Wednesday that officials are looking for ways to send additional troops to Afghanistan this year.

There are at least 140,000 US soldiers in Iraq, about 10 per cent or several thousand more than before the "surge" in late 2007.