BAGHDAD, Iraq – In a surprise visit, Secretary of State Rice and British Foreign Secretary Jack Straw flew here together yesterday and made a dramatic appeal to feuding Iraqi politicians to quickly form a national unity government before the country fractures further along sectarian lines.

“The Iraqi people need their government and leaders,” Ms. Rice told reporters traveling with her and Mr. Straw. “We are going to urge that the negotiations be wrapped up and the government formed.”

Elections were held nearly four months ago and the U.S. Ambassador Zalmay Khalilzad has prodded the Shiite, Sunni, and Kurdish parties to form a unity government. The interim Prime Minister Ibrahim al-Jaafari has sought to retain his post in the permanent government. But American officials view him as weak and ineffectual and have sent signals that he should step down.

Mr. al-Jaafari was narrowly approved by the Shiite bloc, but on Saturday some leaders of that alliance said Mr. al-Jaafari had until yesterday to win over his opponents or he should relinquish the post. Sunni and Kurdish leaders are opposed to Mr. al-Jaafari.

Ms. Rice and Mr. Straw said they were not trying to impose a choice on the Iraqi government and denied they were setting a deadline for action as they spent hours in meetings with virtually all of the top Iraqi leaders. But Mr. Straw, citing “significant international concern” about the protracted process said “they have to make progress to secure a leader.”

Mr. Straw said America “has invested an astonishing amount in Iraq,” in terms of lives lost and expenditures, as has Britain, its main coalition partner. Asked whether support might be reduced, if Iraqi fails to form a unity government, Mr. Straw replied: “We are committed to Iraq, very committed, but we need to see progress and that is in everyone’s interest.”

Ms. Rice added, “There really needs to be a government that is strong and a unifying force for the country that can act on the challenges the Iraqi people face and act on the challenges expeditiously.”

When Ms. Rice and Mr. Straw met with Mr. al-Jaafari yesterday, the tension was noticeable as Ms. Rice sat with a frozen smile on her face and pair made awkward conversation about the weather while reporters were in the room.

By contrast, Ms. Rice bubbled over with enthusiasm when she arrived for lunch at the home of vice president Adil Abdul-Mahdi, who narrowly lost a race with Mr. al-Jaafari to be the Shiite choice for prime minister. “It’s wonderful to see you,” she exclaimed twice.

Shiites and Sunnis have engaged in a bloody cycle of reprisal killings since the bombing of a major Shiite shrine five weeks ago, leading to fears that the country is splintering.

Ms. Rice and Mr. Straw flew here overnight from Liverpool, England, where Mr. Straw had been hosting Ms. Rice during a two-day visit to the region Mr. Straw represents as a member of Parliament. The Iraq war was a contentious issue, with protesters opposed to the American invasion confronting Ms. Rice at almost every stop. Her schedule had called for her to remain overnight in Liverpool on Saturday, but she and Mr. Straw slipped away on her Boeing 757 jet after a reception.