At least 14 Iraqis were killed across the country on Wednesday, and an Iraqi police general, Khodr Abbas al-Salihi, was kidnapped in Baghdad.
The six US soldiers died and six others were wounded in three attacks on Tuesday, the military said.
Four died and six were wounded in an ambush on their patrol vehicles near the northern oil town of Baiji, the military said, adding that attackers set off a mine and opened fire with guns.
The attack was claimed by al-Qaida's frontman in Iraq, Abu Musab al-Zarqawi, according to an unverified internet statement.
A fifth soldier was killed by a car bomber in the capital, while a sixth was killed by small arms fire during combat operations near Habbaniyah in northwest Iraq.
The latest deaths took US military toll since March 2003 invasion to 1834 as of Wednesday, according to an AFP tally based on the Pentagon figures.
A woman grieves for a relative
killed by a bomb in Baghdad
The past three weeks have been one of the bloodiest periods for US forces in Iraq, with about 50 soldiers killed across the war-torn country.
In other violence, six people, including two policemen, were killed and 14 wounded in Baghdad when a suicide bomber drove a car at a police patrol in the west of the capital.
Meanwhile, top Iraqi leaders met in groups to work out their differences over the constitution.
"The Sunnis, the Shiites and the Kurds from the panel met separately with their leaders and will come together tomorrow for a joint meeting," said Mahmud Othman, a member of the constitution-drafting panel.
Prime Minister Ibrahim al-Jaafari expressed hope that the constitution would be ready by 15 August.
"The constitution must be done according to the timetable, just like the way elections and the government were formed," he said.
"It's true that we have only five days left, but I hope we will solve the problems on time," al-Jaafari said, adding that "most parties agreed on federalism."
Issues holding up the constitution include the role of Islam and the scope of federalism, with Kurds insisting on maximum autonomy for their northern region, while Shia and Sunni Arabs remain divided.
Prime Minister Ibrahim al-Jaafari
said he hopes to meet the deadline
Even if the charter is drafted on time, many Iraqis are preoccupied with instability and poor services that their new leaders promised to end when they came to power.
Editorialists in Baghdad's newspapers expressed frustration at the debate among senior leaders and accused them of being out of touch with the concerns of ordinary people.
"People in Iraq are waiting with bated breath for an agreement that brings political stability to this country," wrote Abdelatif al-Moussawi in Azzaman. "But Iraqis today are suffering more than ever from divisions among their leaders."
The editorial in al-Sabah al-Jadeed said: "The time has come for all Iraqis to realise that they are all in this together and that the language of threats and imposing realities will only widen divisions and create civil strife."
Governor's firing retracted
The council of the southern province of Muthanna rescinded its firing of the governor over crackdown on protests in the provincial capital Samawa that killed two and injured 45.
Governor Mohammed Ali Hassani's sacking was illegal because of a technicality, said local government offcial Safaeddine Mohammad Safi, adding he will remain for the time at his post.