More than 250 people have been killed in a series of attacks in recent days, raising fears that Iraqi security forces will struggle to cope after the June 30 withdrawal.
The Iraqi government says the US military has handed over control of 95 per cent of their installations in urban areas to Iraqi forces.
US forces are to leave all cities and major towns of Iraq by the end of June, including Mosul and Kirkuk, where levels of violence remain persistently high.
A "small number" of US troops would be left in some Iraqi cities after the June 30 deadline at so-called Joint Security Stations to train and advise local security forces, a military spokesman said.
The US military will also continue to provide intelligence and air support to Iraqi security forces.
In interviews to US TV stations on Sunday, the US commander in Iraq said the time is right for American forces to pull out of Iraqi cities and expressed confidence in the ability of Iraq's security forces to take more control.
US troops already were out of the country's cities - before Tuesday's deadline - after slowly withdrawing over the last eight months and "overall stability in Iraq remains good", General Ray Odierno said.
He said US forces will "still be conducting significant operations outside of the cities, in the belts of the major cities, and I still believe this will enable us to maintain the current security and stability situation here in Iraq".
Nuri al-Maliki, the Iraqi prime minister, said on Saturday that the transfer of security responsibilities showed that Iraqi institutions were ready to ensure the safety of their own people and would be celebrated as "victory day".
He made the remarks as the Iraqi parliament met to debate the reasons for the apparently deteriorating security situation.
However, Tariq al-Hashimi, the Sunni vice-president, expressed the concerns of many Iraqis when he urged Iraqis, in a statement posted on his website, "to be more cautious and avoid, whenever possible, crowded areas unless there is something important".
'Right to be scared'
Striking a similar cautionary note, Saleh al-Mutlaq, a Sunni member of the Iraqi parliament and the leader of the Iraqi National Dialogue Front, told Al Jazeera: "Iraqis have a right to be scared, they know very well that the withdrawal of American troops from Iraq will leave a political vacuum in the country.
"This is an irresponsible withdrawal from Iraq, because there is not much change in the political process or the American policy in Iraq adopted by the previous US administration.
"Al-Maliki is not aware of the consequences after the American troops leave the country, he wants to deliver what the Iraqis want - an end to the occupation."
Al-Mutlaq's views were echoed by Ayad Allawi, a former Iraqi prime minister, who said that the surge in violence was likely to continue unless "drastic measures" were taken.
"Always we anticipated that once there was a drawdown in forces ... the Iraqi institutions - military and police - are not capable of shouldering the responsibility," he told Al Jazeera on Saturday.
"Nor will the political landscape in the country encourage stability."