The Bush administration is looking to the December elections to produce a permanent and stable Iraqi government after a series of interim administrations, and one that can bridge the sectarian splits evident in last month's constitutional referendum.
The constitution was approved, propelled by resounding "yes votes" by the country's majority Shiite Muslims and ethnic Kurds.
But Iraqi Sunni arabs, many who feel disenfranchised after the ouster of Saddam Hussein, opposed the document and there were "no votes" in three majority Sunni provinces, including Nineva in the north, which Ms. Rice visited briefly Friday when she stopped in Mosul.
In subsequent talks in Baghdad, with Prime Minister Ibrahim Jafari, and with prominent Sunni leaders, Ms. Rice urged broader participation in the election.
At a joint press appearance with the prime minister, Ms. Rice said the United States supports the political process in Iraq but no particular candidate or party, and she insisted that the soundings she made here left her optimistic about the role to be played by the Sunnis.
"The Sunni participation was indeed encouraging in the referendum, but also the activity that has been going on since then," said Ms. Rice. "I've been meeting with non-governmental organizations that are assisting in the political process and they talk about the very active Sunni participation now to form political groupings, to put forward a list, to educate voters, to encourage voter turnout. And so I think that the remarkable thing is that there is such high activity among the Sunni population."
Mr. Jafari said the relatively large Sunni turnout for the referendum was a very positive sign. He said efforts at dialogue continue inside the current National Assembly, and could also be advanced by a pre-election Iraq reconciliation conference proposed by Arab League Secretary General Amr Moussa on a Baghdad visit two weeks ago.
However disputes have erupted over whether figures associated with the Iraqi insurgency should take part in the meeting, and whether Iraq's neighbors including Iran and Syria would be invited.
Mr. Jafari said he could not accept a conference that would be a platform for terrorists or figures from the former Baathist regime. Heard through an interpreter, he also rejected a recent Syrian suggestion that infiltration of insurgent recruits from Syria was partly due to lax border policing by Iraq.
"It is Iraq, and everybody agrees on that, that is the victim of terrorism," said Mr. Jafari. "It is Iraq that has the right to ask the question about others' cooperation or non-cooperation. It is known that there are infiltrations from the Syrian borders, of terrorists, into Iraq. There are also training camps there, and every Iraqi knows that. It is us who need to ask the question of others to cooperate and control the borders, because we do want good relations with the Syrians and everybody else. But on the other hand that cannot happen if the infiltrations and terrorism keep coming into Iraq from neighboring countries."
Secretary Rice called for broader recognition and financial support for Iraq as it moves toward a permanent government and lamented the fact that few Arab countries have set up embassies in Baghdad.
She is expected to pursue that theme Saturday in Bahrain when she attends the second annual Forum for the Future, aimed at promoting political and economic reform in the Middle East and North Africa, and at the inaugural meeting in Jeddah Sunday of the U.S.-Saudi Arabia strategic dialogue.