The visit by the US secretary of state and Jack Straw came a day after members of the ruling Shia Alliance bloc broke ranks publicly and joined calls for Ibrahim al-Jaafari, the prime minister, to step down to improve chances of ending political paralysis.
"The fact that we're going out to have these discussions with the Iraqi leadership is a sign of the urgency which we attach to a need for a government of national unity," Rice told reporters who travelled with the two ministers from Britain.
US and Iraqi officials say a unity government, more than three months after December's election, is vital to avert all-out war after five weeks of increasing violence.
Rice arrived in Baghdad with Straw a day after visiting his constituency in northwest England.
US officials make little secret of doubts about al-Jaafari's ability to unite and lead Iraq. A British official said that Rice and Straw were to meet al-Jaafari, who refuses to stand aside, and other leaders including Jalal Talabani, the president.
Straw said: "We're committed to Iraq, but we need to see progress and that is in everybody's interest."
Pressure is growing on Ibrahim
al-Jaafari to resign
Their efforts follow a visit last month by US senators who urged Iraq's fractious politicians to bury their differences and reach agreement.
Rice said: "This is in many ways a time of testing for the Iraqi nation and for the Iraqi people. They need a government that can act on their behalf in this time of testing."
The move against al-Jaafari, declared publicly by one leader and echoed anonymously by others, came as parties held their latest round of talks on Saturday on a grand coalition with Kurds and Sunnis, who are adamant in their rejection of al-Jaafari.
Although Iraqi officials said they had reached a deal on forming a national security committee designed to share out more responsibilities among Iraq's feuding sects, there were no tangible signs of progress on the personnel of a new government.
Fighting against the US presence
in Iraq persists
That cannot happen, officials say, until there is accord on a prime minister - unlikely to happen while al-Jaafari remains.
US and British officials worry that the political impasse will fuel violence that is becoming more complex as Iraqis wait for their first full-term government since the US and British invasion overthrew the government of Saddam Hussein in 2003.
Sunni fighters, Shia militias and criminal gangs are all overlapping, worsening Iraq'a security problems.
A US diplomat reiterated it was Washington's analysis that al-Jaafari had not scored well on two criteria for prime minister - his ability to unite Iraqis and his competence as a leader. But he said: "We have no preference."
He denied comments from rival Shia leaders that George Bush, the US president, had directly asked them to drop al-Jaafari.
"I call on Jaafari to take a courageous step and set a fine example by stepping down"
Shia Alliance member
"I call on Jaafari to take a courageous step and set a fine example by stepping down," Kasim Daoud, a senior member of the independent group within the Alliance, told Reuters on Saturday.
An aide to al-Jaafari immediately rejected the call.
Al-Jaafari won the alliance nomination in an internal ballot in February by one vote over the candidate of the bloc's most powerful party, aided by Muqtada al-Sadr.
But senior alliance officials, speaking anonymously, said four of seven main groups within the bloc now wanted him to give up the nomination for a second term if, as is likely, he fails within a day or two to persuade Sunni and Kurdish parties to drop their refusal to serve in a cabinet under him.
The United States, anxious for calm that would let it start pulling out its troops, has stepped up pressure for a coalition seen as critical to stemming sectarian violence that has killed hundreds since an important Shia shrine was bombed a month ago.
Privately, rival alliance leaders have been turning against al-Jaafari but the call on Saturday was their first public stand against him. Critics say he has failed to stem violence and bolster the economy in his year as interim prime minister.
Some also view his reliance on al-Sadr, an Iranian-backed cleric, with suspicion.
Dozens of al-Jaafari supporters took to the streets in Baghdad on Saturday, holding a mock funeral with a coffin labelled "Democracy".