To prevent militants from disrupting Thursday's main balloting, the government said it will close its borders, extend a nighttime curfew and restrict domestic travel starting Tuesday.
Iraqi troops at a base in volatile Anbar province marched to a base in Ramadi to cast their ballots, chanting that they were prepared to win the battle against terrorists, reports CBS News correspondent Cami McCormick. They voted Monday because all 2,000 of these Iraqi soldiers will be on duty election day protecting polling places. Their commander says he's confident it will be trouble-free. He's won assurances from local tribal leaders that they will cooperate, but just in case, he'll have men surrounding voting places.
In other developments:
U.S. officials hope the new parliament can help quell the Sunni-dominated insurgency so American forces can begin heading home. The 275-member assembly will be the first fully constitutional parliament since Saddam Hussein's ouster in 2003.
"The reasons for the presence of the multinational forces will start to decrease," al-Jaafari said of the elections.
But he said that a timetable for a withdrawal would also depend on the ability of Iraqi forces to take over security.
"We want the multinational forces to leave, but we don't want security to disappear as well," al-Jaafari said. "When the Iraqi hands are in complete control of the security situation in Iraq, then we will tell the multinational forces, 'Thank you. Please leave the Iraqi lands.'"
A new poll found that most Iraqis disapprove of the presence of U.S. forces in their country, yet they are optimistic about Iraq's future and their own personal lives.
A statement circulated Monday and believed issued by an insurgent group said fighting would continue regardless of the vote, according to residents of a Sunni neighborhood.
The unsigned statement, distributed in the Sunni stronghold of Azamiyah, was written in a linguistic style used by Islamic extremists.
The statement said Sunnis could use the elections to battle corruption and make some political gains but that "fighting will continue with the infidels and their followers."
Monday's early voting saw the first of 1,500 patients cast ballots at Baghdad's central Yarmouk hospital, election officials said.
"There is a big hall for patients who can easily walk and the election committee moves a box around to the wards where there are patients who can't leave their beds," said Yousif Ibrahim, director of the election center.
It was not be the only early voting ahead of general elections.
On Tuesday, the estimated 1.5 million Iraqi voters living outside the country can begin casting their ballots at polling centers in 15 countries. That voting also ends Thursday.
Suspected insurgents held in U.S. or Iraqi detention but who have not been convicted, are eligible to vote, Iraqi officials said. Saddam, who is jailed and facing trial for the deaths of more than 140 Shiites in 1982, also can vote but it is not known whether he would.
Thousands of Iraqi forces will be protecting polling stations, with U.S. and other coalition troops ready to help in case of a major attack.
Most attention has focused on Sunni Arabs, who largely boycotted the Jan. 30 election to protest the continued U.S. military presence. That enabled the Shiites and Kurds to dominate parliament, a move that sharpened communal tensions and fueled the insurgency.
This time, more Sunni Arab candidates are in the race, and changes in the election law to allocate most seats by province instead of based on a party's nationwide total all but guaranteed a sizable Sunni bloc in the next assembly.
Turnout in January was about 58 percent but less than 5 percent in the predominantly Sunni province of Anbar, a hotbed of insurgency.
Even with a big Sunni vote, Shiites are expected to win the biggest share of parliamentary seats. Shiites form an estimated 60 percent of Iraq's 27 million people compared to 20 percent for the Sunni Arabs.