Ms Rice and Mr Straw flew in secretly from Britain under tight security for an unprecedented joint effort to reignite a political process that has dragged on since December’s legislative elections, amid growing sectarian violence.
Bad weather forced the two top diplomats to take overland transport under high security on the dangerous road between the airport and the heavily guarded Green Zone.
Ms Rice told reporters she had "very direct" discussions with leaders of Iraqs Shiite, Kurdish and Sunni communities, including President Jalal Talabani and Prime Minister Ibrahim Jaafari, on the stalled political talks.
"It should be very clear to everyone that the time has come for these negotiations to produce a government of national unity," Ms Rice told reporters accompanying her and Mr Straw from Britain.
"The American people want to see Iraq succeed. But they want to see Iraq progress towards success, and that’s important to the American people as they continue to support this effort," she said.
Mr Straw, making his ninth visit to Iraq, said there was "significant international concern" about delays in the formation of the battered country’s first permanent government since Saddam Hussein was outsted three years ago.
Iraqis have been arguing over Mr Jaafari's bid to stay on as prime minister as the candidate of the Shiite United Iraqi Alliance, which controls nearly half the seats in the 275-member parliament.
The discontent has now spread to Mr Jaafari's own alliance, with several members openly calling for the prime minister to step down to help smooth negotiations among the fractious communal groups.
The latest Shiite to speak out was Jalal Al-Deen Al-Saghir, of the powerful Supreme Council of the Islamic Revolution in Iraq (SCIRI), who told news agency AFP it was time Mr Jaafari let go of ambitions to keep his job.
"I appeal to Jaafari to renounce his candidacy as the country is in a crisis and his candidacy has not been unanimously accepted by the Shiite alliance," he said.
Despite reports the US had soured on Mr Jaafari for his alleged sectarian leanings and failure to crack down on the insurgency, Ms Rice and other US officials were careful not to take any sides in the political jockeying.
But the Secretary of State did point out that Mr Jaafari had failed since his nomination on February 11 to bring together a cabinet.
"The Iraqis need to do that. They’ve got to get a prime minister who can form a government," she said.
US officials see establishment of a government bringing together the majority Shiite Muslims, Kurds and minority Sunnis as the key to an exit strategy for the eventual withdrawal of some 130,000 US troops in Iraq.
"There is pressure on all of us" to form a government, said Adel Abdel Mahdi, who is one possible candidate to replace Mr Jaafari.
Abdel Mahdi, who belongs to the powerful SCIRI party, lost the nomination to Mr Jaafari in February by one vote.
Chopper crash
Underlining the treacherous security situation, the US military announced the deaths of six of its troops across Iraq, including two pilots of a helicopter that crashed on Saturday southwest of Baghdad after coming under hostile fire.
"The two pilots are presumed dead," the military said.
Earlier, an Iraqi insurgent group, The Lions of Islam in the Maath bin Jabal Brigade of Al-Rashideen Army, claimed responsibility for the attack in an unconfirmed statement published on the Internet.
In other incidents, the brothers of Sunni politician Saleh al-Mutlak and Khalaf al-Alyan were kidnapped in separate incidents over the past week, an aide to Mutlak reported on Sunday.
Three other Iraqis were shot dead near Baquba, northeast of Baghdad, and one policeman was killed in the capital. Six bodies were also found in the south of the city.