— In a significant first step toward resolving the issue of future U.S. military involvement in Iraq, top political leaders Tuesday night authorized the Iraqi government to begin negotiations with the United States about keeping military trainers in the country beyond the end of the year.

President Jalal Talabani, Prime Minister Nouri al-Maliki and other top Iraqi leaders met for about five hours to discuss several long-simmering political issues, including the future of U.S. troops in the country.

The leaders agreed that any request to keep U.S. military trainers in Iraq would fall under a general security agreement with the United States and would not require signing a new accord to keep U.S. troops in the country into 2012, according to Talabani’s office.

U.S. military and diplomatic officials in Iraq did not respond to requests for comment Tuesday night.

The decision by Iraqi leaders came as Adm. Mike Mullen, chairman of the Joint Chiefs of Staff, wrapped up a two-day visit to Iraq on Tuesday and called on the country’s leaders to quickly determine whether they want U.S. forces to stay.

Mullen, who met with Talabani and Maliki on Monday, said both leaders “are very aware of the urgency of the issue” for U.S. officials.

“There are some very difficult political challenges, internal challenges associated with reaching this decision,” Mullen said. “That’s really, obviously, up to [the Iraqis] to continue to work towards.”

But Mullen said Iraq should move quickly, because “you get to a point in time where you just can’t turn back, and all the troops must leave. That’s why it’s so important to make the decision absolutely as soon as possible.”

Absent a final decision, the estimated 46,000 U.S. troops in Iraq remain on schedule to withdraw by Dec. 31.

Mullen also reiterated that any agreement to keep U.S. troops in Iraq must include guarantees of legal immunity for American forces.

But that request could prove difficult, as many Iraqi lawmakers, aware of widespread public opposition to a sustained U.S. military presence, are unwilling to grant such protections to American troops.

Mullen was making what is expected to be his last visit to the country before retiring in October.

Speaking from one of Saddam Hussein’s former palaces at a U.S. military base on the outskirts of Baghdad, he once again accused Iran of continuing to arm and train Iraqi insurgent groups that target Iraqi citizens and U.S. troops.

Such actions “are hardly the acts of a friend,” Mullen said.

“It is clear that Tehran seeks a weak Iraq and an Iraq more dependent upon and more beholden to a Persian worldview,” he added.

But he praised Talabani and Maliki for raising concerns with Iranian officials about their country’s alleged support for insurgent groups. The move has helped reduce violence in recent weeks, Mullen said.

Special correspondents Aziz Alwan and Asaad Majeed contributed to this report.