Barack Obama and Iraqi prime minister have met, during the US Democratic presidential candidate first visit to Baghdad, as part of a major foreign tour.
If he is elected president in November, the Illinois senator will advocate pulling out US combat troops within 16 months.
But US commanders, and some members of the Iraqi government, are opposed to setting any timetables.
Shortly after arriving, as part of a US Congressional delegation, the Illinois senator held talks with Nuri al-Maliki, Iraqi prime minister.
The US Democratic candidate is also due to meet president Jalal Talabani as well as Gen David Petraeus, the top US military commander in Iraq, and others.
Flexible on details
While advocating the withdrawal of combat troops, Mr Obama says he is prepared to be flexible on details, and could leave some troops behind for special tasks, like training Iraqi forces and tackling remnants of the al-Qaeda in Iraq group.
Over the next weekend, Mr Obama is visiting a series of countries like Jordan, Israel, Germany, France and the UK, in an attempt to bolster his foreign policy and security credentials.
Barack Obama and Nuri al-Maliki met in Baghdad’s heavily-protected Green Zone, the seat of the Iraqi government, no details were immediately available.
Jack Reed and Chuck Hagel, two Senate Colleagues accompanied Barack Obama. They are long-time critics of the US military’s involvement in Iraq.
According to Susan Rice, one of Mr Obama’s senior foreign policy advisors, he wants Iraq to assume principal responsibility for security.
“We cannot sustain the current high levels of deployment in Iraq indefinitely… without breaking our military”, she told the BBC.
“Nor can we maintain them at high levels in permanent bases with the agreement of the Iraqi government because they’ve been quite clear that they don’t want that.”
Last week, Iraqi prime minister and US president said that they had agreed to set a “time horizon” for the withdrawal of troops, as part of a security pact still being negotiated.
The White House said that any decision to remove troops would be based on “improving conditions”, not an “arbitrary date”.
The leaders of Iraq’s governing coalition are under pressure to show movement towards sovereignty, said the BBC’s Jim Muir, in Baghdad.
In forthcoming provincial elections they risk to be outflanked by more militant elements, who are calling for an immediate withdrawal of foreign forces, like the group led by the radical Shia cleric, Moqtada Sadr, BBC’s correspondent says.
More troops to Afghanistan
Even though frequent attacks continue throughout the country, violence in Iraq is at its lowest level since 2004. Last week, in two separate twin suicide bombings, some 50 people died.
Before his visit, Barack Obama said that some of the troops withdrawn from Iraq ought to be sent to Afghanistan, in order to reinforce efforts there against a resurgent Taleban and to control spiralling violence.
“We have to understand that the situation is precarious and urgent and I believe this has to be the central focus, the central front, in the battle against terrorism”, he told the CBS programme, Face the Nation.
The US needed to start planning immediately to send in more troops and called for an extra one to two brigades in Afghanistan, he said.
Barack Obama has been criticised by John McCain, his Republican rival, for announcing a strategy before visiting the region and for setting a date for a US withdrawal from Iraq.
Randy Scheunemann, Mr McCain’s foreign policy adviser said that the Democratic candidate was “stubbornly adhering to an unconditional withdrawal that places politics above the advice of our military commanders”.