Although an intense sandstorm forced meetings to be cancelled on Monday and brought delays on Tuesday, substantive talks were held, said Kamaran Garadaji, a spokesman for Prime Minister Ibrahim al-Jaafari.
Garadaji said the leaders at the meeting were determined to reach an agreement ahead of the 15 August deadline.
One of the key issues holding up the constitution is the scope of federalism, with Kurds insisting on maximum autonomy for their northern region, while Shia and Sunni Arabs are divided over whether other provinces should also get autonomy.
US ambassador Zalmay Khalilzad assured reporters that while the Kurds wanted autonomy, they would not be pushing for independence.
"Barzani himself has said that while the Kurds have the right to self-determination, they have decided not to exercise that ... the issue is not on their agenda," the ambassador said.
Iraqis demonstrated to demand the
resignation of Alaa al-Tamimi
"There are some issues over the role of Islam and whether it should be 'a main source' or 'the main source' of legislation," he said.
Kurdish leader Massoud Barzani, who had been unable to fly in from northern Iraq due to the bad weather, arrived late on Tuesday and was set to participate in talks on Wednesday, a Kurdish member on the constitution-drafting panel said.
Iraqi government spokesman Laith Kubba said on Tuesday morning that the question of the rights of women, much debated by the Western press, was not a great problem.
A small group of conservative Iraqi women mounted a counter demonstration to one organised by 50 of their liberal opponents in central Baghdad on Tuesday over the issue of women's rights.
"We want the constitutional drafting committee to hear our voices," said Environment Minister Narmine Othman, associated with the liberal group. "We fear that some articles will be unjust for women."
Counter-demonstrator Fadia Al-Aaraji, carrying a banner stating the rights of Iraqi women were guaranteed by Islam, said: "We are demanding that the Iraqi people's Islamic identity be respected and included in the constitution."
A driver in a booby-trapped car drove into a US convoy waiting at an intersection on Tuesday in central Baghdad, killing at least three people, including one American soldier, and wounding at least 52.
A US marine assigned to the 2nd Marine Division was killed on Monday by small arms fire in Ramadi, 110km (70 miles) west of Baghdad, the US military said on Tuesday.
Fighters have shot dead two
police officers in Baghdad
At least three of the attacks, most of them in Baghdad, were claimed by the group headed by al-Qaida's front man in Iraq, Abu Musab al-Zarqawi.
The latest deaths brought the number of US service members killed in Iraq this month to 32. .
At least 10 Iraqi police officers were shot dead in five attacks in Baghdad, an Interior Ministry official said.
The governor of Baghdad, who vowed to save the broken city after Saddam Hussein's fall, seemed himself to have fallen victim to its growing chaos on Tuesday, saying gunmen ousted him and installed a rival.
Alaa al-Tamimi said he was not at his office at the time but 120 gunmen installed Hussein al-Tahhan in his place on Monday.
A policeman walks past the
debris of a car bomb in Baghdad
His account of events could not be immediately confirmed and was challenged by al-Tahhan, who is governor of the governorate of Baghdad, which includes the city and its suburbs.
Only one thing is clear. Confusion reigns at city hall.
"I am appointed by the state," al-Tamimi said. "I handed in my resignation three times because I knew there would be trouble. Acts like these set a very dangerous precedent for a country that wants to be free and democratic."
The secular-minded engineer said the Shia Islamist-dominated Baghdad provincial council had been keen to replace him since it was elected in January, mirroring power struggles that have fractured the national government.
Shia and Kurds came to power in January elections while Arab Sunnis dominant under Saddam have not boycotted the elections in a new political landscape fraught with sectarian tensions.
Denying that he entered the offices by force, al-Tahhan said he had made a routine arrangement to meet the governor's staff.
"I was greeted at the door by the Deputy Mayor Amir al-Su'aidi. He led me in person to the office and I told my guards to stay outside," he said.
"It's absurd to think I could force my way in. I only came with five Land Cruisers. The whole governorate only has 15, while he [al-Tamimi] has 100 personal guards."
Who is the governor?
Uncertainty over who is mayor is not new. Before al-Tamimi took office, US soldiers briefly arrested self-proclaimed postwar governor Muhammad al-Zubaidi for exercising authority they said he did not have.
Al-Tamimi returned to Baghdad from years in exile in the oil-rich Gulf emirate of Abu Dhabi vowing to rescue a city battered by wars and United Nations sanctions under Saddam.
"We want the constitutional drafting committee to hear our voices, We fear that some articles (in the constitution) will be unjust for women"
Armed with a $75 million annual budget and 9000 employees left from Saddam's days, he vowed to clean up city hall.
"We hope Baghdad will return to be the mother of the world," he once said of a city that is now sliding deeper into car and human bombings, assassinations, kidnappings and rampant crime.
Al-Tahhan - a member of a leading Shia Islamist party - did not confirm whether he had replaced al-Tamimi but said the Shia-led council has the authority to force him out: "Baghdad provincial council can replace him because he was appointed by Baghdad's council."