Jack Straw and Condoleezza Rice praised Grand Ayatollah Ali al-Sistani for his guidance - he is the spiritual leader of much of Iraq's Shia population.
They also urged Iraqi politicians to overcome their differences and choose a strong figure to unify the country and restore stability.
At a press conference on Monday at the end of their unannounced visit to Baghdad, Rice said: "We came here to give momentum to the process that is already under way. It is not my responsibility or of Mr Straw to determine who is going to be the prime minister of Iraq.
"That will be determined by Iraqis. But we need a strong, unifying government led by someone who can bring stability and meet the challenges of Iraqi people."
Their visit in the midst of a political vacuum in the country brought on by the lack of a new government came even as the dominant conservative Shia coalition asked US leaders to stop meddling in Iraqi affairs.
Rice told reporters that Iraqi leaders were under pressure from their own people to form a new government for the next four years and "that process has to take place quickly".
"Without the remarkable spiritual guidance shown by his eminence, the Grand Ayatollah Sistani, this country for all its problems it now faces would not have in its hands the potential for a better future"
Jack Straw, the British foreign secretary
The US secretary of state said: "If you do not have the key positions determined, it will be difficult to form the government ...
"You cannot have a circumstance where there is a political vacuum in a country like this that faces so much threat of violence."
Straw emphasised a degree of impatience in America and Britain after more than three months since legislative elections.
"We recognise that coalition always takes time. But this is now taking more than that," he said.
Pressure has been building up on Ibrahim al-Jaafari, the dominant Shia bloc's candidate for prime minister, to quit and pointed remarks by Rice and Straw suggest that they would also like to see the back of him.
On Monday, Jalal al-Deen al-Saghir, of the Supreme Council of the Islamic Revolution in Iraq (SCIRI), joined the calls.
"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 Shia alliance," he said.
Although irritated by the lack of progress by politicians, Straw had nothing but praise for Grand Ayatollah Ali al-Sistani, the spiritual leader for many of the country's majority Shias. He paid tribute to his help in building a new Iraq, and suggested that he could help break the political deadlock.
"Without the remarkable spiritual guidance shown by his eminence, the Grand Ayatollah Sistani, this country for all its problems it now faces would not have in its hands the potential for a better future," Straw said.