BAGHDAD, Iraq — Iraqi leaders said Monday they are seriously considering three-way summit talks with Iran and Syria, responding to an overture from Iran’s president that raises new questions about the ongoing level of American influence over events here.

The talks would focus on how the two neighbor states could help quell sectarian bloodshed in Iraq, according to Iraqi officials familiar with Iranian President Mahmoud Ahmadinejad’s offer.

The invitation to a summit meeting is a further assertion of Iran’s influence and comes when the U.S. government is sharply divided over whether to make its own opening to Iran and Syria. Influential figures in Washington have urged the Bush administration to talk with both countries in hopes of gaining their help in bringing the violence in Iraq under control. But many of Bush’s advisers oppose that idea. Administration policy has been to isolate Iran in hopes of compelling the government to abandon its nuclear program and to refuse to talk with Syria until that nation drops its support for groups the United States considers terrorist.

As the debate continues in Washington, the Iranians have stepped forward. Iraqi president Jalal Talabani plans to travel to Tehran on Sunday to meet with Ahmadinejad and try to iron out details of a possible three-way meeting with Syrian president Bashir Assad, senior Iraqi officials said Monday. That move came as Iraqi Prime Minister Nouri al-Maliki and Syrian Foreign Minister Walid Moallem announced an agreement to reopen diplomatic relations, which were broken off in 1982.

In Washington, State Department spokesman Tom Casey sought to play down the significance of possible three-way meetings, contending that past statements by Iranian and Syrian leaders have not proved productive.

“What we’d like to see the Iranian government do is desist, first and foremost, from negative actions it’s taken in Iraq,” Casey said. “As we have always said with respect to the Syrians, you know, the problem is not what they say, the problem is what they do.”

Syria has served as an entry point and refuge for Sunni Arab insurgents who have waged a steady stream of attacks on U.S. forces and the fledgling Iraqi government since the American-led invasion of Iraq in 2003. Iran, a Shiite Muslim nation, holds strong sway over the Shiite militias that have increasingly attacked Iraq’s minority Sunnis in retaliation.