Iraqi leaders said Tuesday that they need U.S. military trainers to stay beyond a year-end deadline for American forces to leave but that the troops should not be granted immunity from prosecution.

The late evening announcement was significant in that the Iraqi leaders were clear on the need for further help. But it raised questions about the feasibility of ironing out an agreement when the immunity of American troops remains such a contentious issue.

"The head of the political blocs met today ... to discuss the training of Iraqi forces with the help of the American side," said Deputy Prime Minister Roz Nouri Shawez in a statement after the meeting held at the home of Iraqi President Jalal Talabani.

"The leaders agreed on the need to train the Iraqi forces and to complete equipping the force as soon as possible," he said, flanked by some of the main Iraqi political leaders.

But Shawez said the blocs did not want to give troops immunity, as has been demanded by the U.S.

"The heads of blocs agreed on the necessity of not granting the immunity," he said, adding that the training should occur only on Iraqi bases.

The political coalition loyal to anti-American cleric Muqtada al-Sadr objected to any American presence.

"From the first meeting as a Sadrist Trend we showed our absolute rejection to keeping of the forces whether it is as trainers or others, whether it is with immunity or without immunity, and this rejection is fixed forever," said Sadrist Bahaa al-Araji.

Iraqi political leaders have been wrestling for months with whether to ask some American forces to stay past their Dec. 31 departure date. There are currently about 43,500 American troops in the country. Under a 2008 security agreement, all are required to leave by the end of this year.

Privately, Iraqi and American leaders acknowledge that Iraqis still need help with certain tasks such as defending their borders and airspace. But publicly, most Iraqi leaders except for the Kurds have tried to distance themselves from any request for American help since it is an extremely unpopular stand in a country that has gone through nearly nine years of warfare.

Iraqi leaders announced back in August that they were opening talks with the United States on having some sort of training presence in the country past this year. But there has been little traction since then as the U.S. military continues to draw down its forces.