Over the weekend Obama visited Afghanistan, the second front in the US's so-called "war on terror", and where the US has more than 36,000 troops stationed to combat growing violence.
Before touching down in Baghdad, Obama had paid a brief visit to the southern Iraqi city of Basra after spending Sunday night in neighbouring Kuwait.
He is due to arrive in Jordan later on Monday where officials say he will hold talks with King Abdullah.
John McCain, Obama's Republican rival for the US presidency, has criticised Obama for only visiting Iraq twice, and said on Monday he hoped the Illinois senator would see during his visit that he had been wrong to oppose the so-called US troop surge in Iraq last year.
|McCain said Obama had "badly misjudged" the situation in Iraq [AFP]
"I hope he will have a chance to admit that he badly misjudged the situation and he was wrong when he said that the surge wouldn't work. It has succeeded and we're winning the war," he said.
Obama has called for the gradual withdrawal of US troops at the rate of one or two brigades a month, as well as an end to combat operations within 16 months.
He has said he favours leaving a residual force in the country to provide security for US personnel, to train Iraqis and to counter attacks by al-Qaeda.
The Obama campaign has said the aim of his tour is to make an on-the-ground assessment of conditions in the country, as well as meeting leaders, whom he has previously criticised for not doing enough to rebuild Iraq.
"Iraq's leaders have failed to invest tens of billions of dollars in oil revenues in rebuilding their own country, and they have not reached the political accommodation that was the stated purpose of the [US troop] surge," Obama wrote in the New York Times newspaper last week.
Obama was joined on his trip by Jack Reed and Chuck Hagel, Democratic and Republican senators.
Al-Maliki had also recently commented in a German magazine endorsing Obama's 16-month timetable.
However, his aides later said his remarks were misunderstood, and claimed that he is not taking sides in the upcoming US election.
Al-Maliki and George Bush, the US president, have agreed on a so-called "time-horizon" for the withdrawal of US forces as part of a wider security pact still being negotiated.
Obama called the situation in Afghanistan "precarious" and urgent", in an interview with CBS news on Sunday from the country.
He also said he considered the failure to "finish the job" in Afghanistan after the September 11 2001 attacks "one of the biggest mistakes we've made strategically", as Iraq became a distraction.
Obama also pledged to downsize the number of US troops in Iraq and
commit at least two more combat brigades to Afghanistan.
However, he criticised Hamid Karzai, the Afghan president, for having "not gotten out of the bunker" and worked more to improve the lives of Afghan civilians.
The Democratic presidential candidate has made Afghanistan a centrepiece of his proposed strategy for dealing with so-called "terror threats" to the US.
He has said the war in Afghanistan, where the Taliban group has been resurgent, deserves more troops and attention than the conflict in Iraq.
US military officials say the number of attacks in eastern Afghanistan, where most of the foreign troops are American, has increased by 40 per cent in 2008 compared to the same period in 2007.