Iraqi leaders say they want U.S. military trainers to stay in the country beyond a year-end deadline for American forces to leave, but without granting them immunity if they commit crimes – a key condition set by Washington for any deal.

Deputy Prime Minister Roz Nouri Shawez announced late Tuesday that Iraq's main political blocs had agreed “on the need to train Iraqi forces” and equip them as soon as possible. But he said the power-sharing government's Shi'ite, Sunni and Kurdish factions do not want to give U.S. troops immunity, and he added that the training should take place only on Iraqi bases.

This decision allows Iraqi Prime Minister Nouri al-Maliki to continue discussions about keeping some U.S. forces in the country after the 2011 deadline for their withdrawal – more than eight years after the invasion that toppled former leader Saddam Hussein.

The political coalition loyal to anti-American cleric Muqtada al-Sadr – which objects to any U.S. presence in Iraq – rejected the idea outright.

The United States wants its troops to have legal protections similar to those afforded them under the current security arrangement. That would mean allowing Iraq some jurisdiction over American forces for certain crimes committed outside duty. But the U.S. would get prime responsibility for crimes committed during duty or on its bases.

There are now approximately 43,500 U.S. troops in Iraq. Under the 2008 security arrangement, all are required to leave by the end of the year.