Rice, the most senior US official to visit since Iraqi Prime Minister Ibrahim al-Jaafari formed his government, first arrived in Arbil in northern Iraq to meet Kurdish leader Massoud Barzani before moving on to Baghdad.
Asked about the importance of drafting a new constitution by a 15 August deadline, Rice said: "Things do not happen overnight."
"We have become very impatient people. Iraq is emerging from a long national nightmare of tyranny into freedom."
The new constitution to be drafted by al-Jaafari's government and the National Assembly will be the basis for December 2005 elections.
Reaching out to Sunnis
US National Security Adviser Stephen Hadley said Rice's trip was part of a US effort to reach out to Sunni Muslims.
"Obviously, she is going to continue that process, because that is really the way forward over the long term to bringing a conclusion to this terrorist effort," Hadley told CNN.
The Iraqi PM is battling to restore
law and order in the country
Al-Jaafari said he wanted the drafting of the constitution to be an inclusive process that involved Sunni Arabs as much as possible.
"We will try to find ways to have a bigger Sunni participation," he said.
Rice supported his position telling CNN: "If there is to be a united Iraq in the future, then Sunnis have to be included in the processes going forward and just as they've been included in this government."
Rice discussed speeding up the training of Iraqi forces to take on greater security duties.
"If there is to be a united Iraq in the future, then Sunnis have to be included in the processes going forward and just as they've been included in this government"
US secretary of state
"We are fighting a very tough set of terrorists who are, it seems, determined to stop the progress of the Iraqi people," Rice said.
She claimed the US was determined to move ahead with the political process and undercut the violence.
More than 400 people have died since the new cabinet was named on 28 April.