Asking U.S. forces to stay in the cities, including volatile Mosul in the north, would be embarrassing for Iraq's prime minister, who has staked his political future on claims that the country has turned the corner in the war against Sunni and Shiite extremists.
The departure of heavily armed combat troops from bases inside the cities is important psychologically to many Iraqis, who are eager to regain control of their country after six years of war and U.S. military occupation.
U.S. officials played down the Iraqi decision, with Pentagon spokesman Bryan Whitman saying it's up to the Iraqi government to request an extension of the U.S. presence in the cities and "we intend to fully abide by" terms of the security agreement.
The chairman of the Joint Chiefs of Staff, Adm. Mike Mullen, told reporters Monday that violence had not risen to a level that would force a change in the withdrawal schedule.
Last month, however, the top U.S. commander in Iraq, Gen. Raymond Odierno, said he was worried that Iraqi forces won't be ready to assume full responsibility for Mosul by the end of June.
Privately, some U.S. officers fear the Iraqis may lose control of Mosul within a few months after American forces pull out of Iraq's third largest city, where al Qaeda and other Sunni militants remain active.
The U.S.-Iraq security agreement that took effect this year calls for American combat troops to leave urban areas by the end of June, with all U.S. forces out of the country by the end of 2011.
But a series of high-profile bombings has raised questions whether Iraqi forces can assume more security responsibilities, especially in Mosul.
Nationwide, at least 451 people were killed in political violence last month, compared with 335 in March, 288 in February and 242 in January, according to an Associated Press tally.
Even in Baghdad, where violence is down sharply from levels of two years ago, attacks are continuing.
On Monday, two car bombs exploded almost simultaneously near the Oil Ministry and a police academy, killing at least three people and wounding eight.
Although those casualties were relatively low, the attack was significant because it occurred in a sensitive, well-guarded area in the heart of the Iraqi capital.
The security agreement allows Prime Minister Nouri al-Maliki to request an extension of the deadlines if he feels Iraqi forces need help. But the prime minister's spokesman said the withdrawal deadlines, including the June 30 date, were "non-extendable."
"These dates cannot be extended and this is consistent with the transfer and handover of responsibility to Iraqi security forces," spokesman Ali al-Dabbagh said in a statement.
Kurdish officials would prefer to keep U.S. troops in Mosul after the deadline.
"I have doubts about security and stability in Mosul," Kurdish politician Saadi Ahmed Pera said. "Therefore, U.S forces should stay in Mosul until all the pending problems among political groups in the city are solved."
However, many other key Iraqi politicians, including the newly elected leadership in Mosul, oppose keeping U.S. combat troops in urban areas after the June deadline.
Al-Maliki, a Shiite, needs the support of the Sunni leadership in Mosul as he prepares for national elections by the end of the year.
The new governor of the Mosul area told the AP on Monday that the departure of U.S. troops from the city will actually reduce violence, since much of it is directed at the Americans.
"A U.S. withdrawal will reduce the number of targets," Gov. Atheel al-Nujaifi said. "We believe it's important for U.S. troops to stay in camps outside the cities to provide help only if needed."
The requirement to leave the cities applies only to combat troops and not to trainers, advisers and others in noncombat roles. The agreement does not preclude combat soldiers from patrolling in Baghdad, Mosul and other cities from bases outside the city limits.
But prominent Shiite lawmaker Abbas al-Bayati said extending the June 30 deadline would "send the wrong signal to the Iraqi people" that the Americans might remain in the country indefinitely.
"Thus both sides must stand together to fulfill the withdrawal timetable," he said.
U.S. combat troops largely pulled out of many cities in 2005 and 2006 but returned a year later as part of the U.S. troop surge that was designed to protect civilians from Shiite and Sunni extremists living in their neighborhoods.
This time, U.S. and Iraqi officials are gambling that Iraqi security forces are better trained and equipped to prevent the return of extremists than they were years ago.
Extending the deadline would also call into question al-Maliki's claim that his government has set the country on the road to stability - despite the occasional spike in violence.
On Monday, al-Maliki told an audience in Paris that he would not allow Iraq to be used as a "base for any terrorist organization" and that the country was ready for foreign investment.
Nevertheless, U.S. officials believe security in Iraq remains fragile because the various religious and ethnic groups have still not agreed on power-sharing arrangements necessary for long-term stability.