Voting abroad began first in Australia on Tuesday, where up to 20,000 registered Iraqi voters live.
They are part of a group of 1.5 million voters living outside Iraq who will cast ballots at polling centres in 15 countries, including the United States, Canada and the Netherlands.
The expatriates will help elect the 275-member National Assembly, which will legislate in the coming four years and choose the first fully constitutional government in Iraq since the overthrow of Saddam Hussein's government in 2003.
"I hope this leads to democracy in Iraq and freedom for its people," said Mawahib Muhammad, 32, a college student and a Shia Muslim from southern Iraq who cast her ballot at a London station.
Iraqis living in France were being asked to go to Amsterdam, in the Netherlands, to cast their ballots.
Iraqis living in Denmark and southern Sweden cast ballots in Copenhagen amid heavy security.
Iraqis who lined up to vote in Berlin seemed jovial but cautiously optimistic.
Many of the 50 or so who waited outside a makeshift security checkpoint in the loading dock of a former mail distribution centre were part of a group from Poland that had chartered a bus to make the nine-and-a-half-hour journey to Berlin on Monday.
A leading Sunni Muslim Arab politician has been shot and killed in Iraq two days before the nation votes for a new parliament.
Mizhar al-Dulaimi, leader of the Free Progressive Iraqi Party, was killed on Tuesday while campaigning in the centre of Ramadi, capital of the restive al-Anbar province in western Iraq, police said. Three of his bodyguards were wounded.
"I hope this leads to democracy in Iraq and freedom for its people"
Iraqi emigrant in London
Al-Dulaimi had appeared on television the previous night, urging Iraqis to vote.
Many Sunni Arabs are standing in Thursday's poll after mostly boycotting the 30 January election for an interim assembly.
Al-Qaida and four other groups on Monday described the election as ungodly and said they would continue fighting until they had turned Iraq into an Islamic state, but they did not threaten to disrupt the voting.
Another group has told its members not to attack polling stations during Thursday's legislative elections to avoid killing civilians, according to a statement published on Tuesday in the group's name on the internet.
The group, the Islamic Army in Iraq, said the move did not mean it supported the political process in Iraq and vowed to continue attacking foreign and Iraqi forces.
"To the heroes of the Islamic Army in Iraq: Orders have been issued to avoid polling stations centres to preserve the blood of innocent people"
Islamic Army in Iraq
In its internet statement, the group addressed its fighters saying: "To the heroes of the Islamic Army in Iraq: Orders have been issued to avoid polling stations centres to preserve the blood of innocent people."
The statement could not be independently verified, but it appeared on a website known for carrying such material.
The group said the orders were in line with its policy of not shedding the blood of innocent people. "It does not mean our support for the political process," but rather a commitment to Islamic rules, the statement added.
The Islamic Army said it captured the former US marine and civilian contractor, Ronald Allen Schulz, saying he was working as an "American security consultant for the Housing Ministry".
Last Thursday, it claimed to have killed Schulz because the US failed to respond to its demand for the release of Iraqi prisoners. Schulz's body has not been found.