This would be first such round of multilateral diplomacy since the 2003 US-led invasion.
Shift in policy
Completing a shift in US policy, Rice is expected to talk to Syria and Iran, who have been accused by Washington of funding and abetting Iraq's Sunni uprising and Shia militias respectively.
A rumoured meeting with her Iranian counterpart, Manouchehr Mottaki, would mark the highest-level official contact between the two foes since the US cut relations in 1980.
However, Tehran has yet to give an unequivocal sign it is ready for talks, and Mehdi Mostavafi, the deputy foreign minister, said on Tuesday the conditions were not right for a "dialogue" with Rice at the conference.
Speaking during a stopover in Ireland, Rice indicated she would be ready to discuss issues other than Iraq with the Iranian foreign minister, including the standoff over the Islamic republic's nuclear programme.
She said: "I think I could handle any question as asked."
'Negative effect'
Hoshyar Zebari, the Iraqi foreign minister, said during a visit to Tehran last week: "The developments between Iran, the United States and the West have had a negative effect on Iraq's situation, and the more they have dialogue together the more it will help the Iraqi government's efforts to succeed."
In the run-up to the landmark conference, Western and regional leaders have hammered home the same message that Iraq's influential neighbours need to do their share.
On Sunday, al-Maliki again warned his neighbours that the "terrorist attacks that target Iraq are not limited to Iraq, but will spread to every country in the world".
As some of the 27 foreign ministers and diplomats representing 22 other countries were expected to start arriving, Egyptian police imposed a tight security cordon around Sharm el-Sheikh.