The agenda includes a five-year plan for financial and political support for Iraq, and ways to end sectarian violence.
But today much of the attention was focused on a meeting between Rice and Syrian Foreign Minister Walid al-Muallim.
Rice and al-Muallim met for about a half-hour on the sidelines today to discuss how to stabilize Iraq.
Afterward, al-Muallim characterized the session as "frank and constructive." He added, "We discussed the situation in Iraq, how to achieve stability and security in Iraq. And we discussed also bilateral relations between Syria and the United States."
It's been more than two years since the two countries have conferred at such a high level.
A 'Businesslike' Meeting
The United States accuses Syria of supporting Hamas and Hizballah terror attacks against Israel and allowing fighters to cross its borders to join the Sunni insurgency in Iraq.
But shortly before the meeting at Sharm el-Sheikh, General William Caldwell, the chief U.S. military spokesman in Baghdad, said that for the past month or longer, Damascus had tightened its border security and that, quote, "there has been a reduction in the flow of foreign fighters into Iraq."
Rice said she and al-Muallim discussed the problem of foreign fighters in Iraq, and called their meeting "professional" and "businesslike."
The very fact that Rice and al-Muallim met is viewed as significant, even if they didn't resolve any issues.
U.S. - Iran Meeting Uncertain
There are reports that Rice may still meet with Iranian Foreign Minister Manouchehr Mottaki, although nothing has been scheduled yet.
At first, there was even a question whether Mottaki would attend the conference. Last week, however, he said he would. But on arrival in Sharm el-Sheikh today, he chastised the United States. "The security situation in Iraq, which is primarily caused by the flawed policies of the occupying powers, overshadows efforts to deal with other issues," he said.
Washington takes the opposite view. It accuses Iran of arming Shi'a militias that are not only fighting against U.S. troops but also with Sunni militants, raising fears of increasing communal warfare in Iraq.
The two countries also have deep differences over Iran's nuclear program, through Washington has said any talks would focus on Iraq.
The United States and Iran have had no significant contact since they broke off relations over the hostage taking of U.S. diplomats in Tehran after the 1979 Islamic Revolution.
International Compact Set For Adoption
Today's opening session of the conference is focused on a five-year plan sponsored by the UN called the International Compact With Iraq, or ICI. It's designed to help with development and reconstruction, aid and investment, and debt relief.
UN Secretary-General Ban Ki-moon emphasized the need for an international effort to stabilize Iraq.
"I cannot leave Iraq on its own to meet the enormous challenges that it faces," Ban said. "The international community as a whole, and in particular Iraq's neighbors and regional countries, must work together to help Iraq build a peaceful, unified, and prosperous country."
Iraqi Prime Minister Nuri al-Maliki said at the opening session that Iraq is concerned about the amount of debt it owes.
"We call upon all our friends and brothers who are taking part in this conference to eliminate the debts of Iraq so Iraq can start building, reconstruction, and development projects and start rebuilding destroyed infrastructure," he said.
Iraq's finance minister, Bayan Jabr Solagh, told AFP news agency before the conference began he expected countries, including Saudi Arabia and Egypt, to write off as much as $40 billion to $50 billion worth of debt at the meeting.
The conference is expected to adopt the ICI later today.
Iraq Grateful For Support
Tomorrow's session is expected to focus on security in Iraq, and is likely to be less harmonious. Already, Mottaki has blamed the violence in Iraq on the presence of foreign forces.
But the Iranian foreign minister added that his government is as concerned as any other participant about stability within its neighbor's borders.
"We do believe [that] all the parties -- everybody -- should support Iraq [in achieving] stability, security in that country," Mottaki said.
Iraqi Deputy Prime Minister Barham Salih, speaking to reporters on the sidelines of the conference, said he's grateful that so many influential nations have sent representatives to the conference to try and help Iraq.
"We consider Arab, Iranian, [and] American understanding and support for Iraqi transition as an important development," he said.
Salih was asked if his government has tried to get Rice and Mottaki together at Sharm el-Sheikh, but he brushed aside the question. Even if Rice and Mottaki don't meet, he said, their presence alone is encouraging.
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Al-Sadr supporters demonstrating against the U.S. presence in Iraq in October 2006 (epa)
A RADICAL CLERIC. Shi'ite cleric Muqtada al-Sadr is a key figure in Iraq. He heads the Imam Al-Mahdi Army militia and a political bloc that is prominent in parliament and the government. His ties to Iran have also provoked concerns in some quarters.