BAGHDAD — Iran agreed yesterday to join America 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 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 Egypt conference will also include Secretary of State Rice, raising the possibility of a rare direct encounter between high-level American and Iranian officials. In Washington, Ms. 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,” Ms. Rice told ABC’s “This Week.”