The pair travelled from the UK, where Mr Straw hosted Ms Rice's two-day trip. They are expected to meet PM Ibrahim Jaafari and President Jalal Talabani.
The visits come as Iraqi politicians struggle to form a government of national unity.
Ms Rice said the US regarded the formation as a "matter of urgency".
Mr Straw added: "We need to see progress and that is in everybody's interest."
The visits come amid mounting pressure on Mr Jaafari, of the majority Shia alliance, to stand down as prime minister.
He has failed to win the support of minority Kurds and Sunnis and now faces opposition within his alliance.
Last week senior Shia politicians said US ambassador to Iraq, Zalmay Khalilzad, had told them President George W Bush "doesn't want, doesn't support, doesn't accept" the retention of Mr Jaafari.
Mr Jaafari responded by saying the comments undermined Mr Bush's commitment to democracy in Iraq.
Speaking to reporters travelling with her to Iraq, Ms Rice said: "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."
Her comments echoed those made by Mr Khalilzad on Saturday.
Ibrahim Jaafari has come under pressure to step down as PM
He said: "This government needs to have a good programme to govern from the centre and needs good ministers who are competent.
"Iraq is bleeding while they are moving at a very slow pace."
Mr Jaafari was chosen as PM by the ruling Shia-led bloc after it won December's election.
But Kurdish and Sunni Arab parties have rejected the nomination and have threatened to boycott a government unless he withdraws.
The delay in forming a government is thought to be partly responsible for fuelling the increasing sectarian violence which has struck Iraq since last month's bombing of a key Shia shrine at Samarra.
Ms Rice arrived in Iraq after a testing trip to the UK.
She admitted the US had made thousands of tactical errors in Iraq, but later said she was only speaking figuratively.
She also had to face a number of anti-Iraq war protests in north-west England.
Source: BBCLast Mod: 20 Eylül 2018, 18:16