Baghdad, Iraq ? Iran agreed Sunday to join the U.S. and other countries at a conference on Iraq this week, raising hopes the government in Tehran would help stabilize its violent neighbor and stem the flow of guns and bombs over the border.

In an apparent effort to drive home that point, Prime Minister Nouri al-Maliki told an Iranian envoy that the persistent violence in Iraq – some of it carried out by the Shiite militias Iran is accused of arming – could spill over into neighboring countries, including those that are “supposed to support the Iraqi government.”

Iraq’s other neighbors as well as Egypt, Bahrain and representatives of the five permanent U.N. Security Council members have agreed to attend the meeting Thursday and Friday in the Egyptian resort of Sharm El-Sheik.

The conference also will include Secretary of State Condoleezza Rice, raising the possibility of a rare direct encounter between high-level U.S. and Iranian officials.

In Washington, Rice would not rule out a meeting with the Iranians, whose delegation will be led by Foreign Minister Manouchehr Mottaki.

“But what do we need to do? It’s quite obvious. Stop the flow of arms to foreign fighters. Stop the flow of foreign fighters across the borders,” Rice told ABC’s “This Week.”

Hours earlier, al-Maliki’s office announced that Iranian President Mahmoud Ahmadinejad had telephoned to say a delegation from his country would attend the conference.

Iraqi leaders had been pressing for the Iranians to attend the Egypt meeting for weeks, but Iran refused to commit, in part because of fears that it would come under pressure from the U.S. and others about its nuclear program.

In addition, the Iranians have been lobbying for release of five Iranians held by the U.S. in Iraq since January. The U.S. has accused the five of links to an Iranian Revolutionary Guard unit that arms and trains Shiite extremists in Iraq and elsewhere in the Middle East.

The decision to attend “came after consultations between Iraqi officials and the Iranian president,” Foreign Ministry spokesman Mohammad Ali Hosseini said.

Senior Iranian envoy Ali Larijani flew to Baghdad on Sunday for talks with al-Maliki and other senior Iraqi officials – the highest-ranking Iranian official to visit Iraq since the collapse of Saddam Hussein’s regime in 2003.

During their meeting, Larijani told al-Maliki that all countries that want stability in the region “have no choice but to support Iraq’s elected government.”