George Bush, speaking at a news conference with Nuri al-Maliki in the Jordanian capital Amman on Thursday, also said the Iraqi leader told him that any partition of Iraq would only increase violence.
Bush said: "He is a strong leader and wants a free and democratic Iraq to succeed."
He praised al-Maliki as the "right guy" for the job.
"We are going to help him and it is in our interest to help him for the sake of peace," Bush said.
"He is a strong leader and wants a free and democratic Iraq to succeed.
"The first thing that gives me confidence is that he wants responsibility," Bush said referring to the Iraqi prime minister's calls for security control over Iraqi provinces to be transferred to Iraqi forces more swiftly.
"What I appreciate is his attitude. Instead of saying America you go solve the problem we have a prime minister who says: 'Stop holding me back, I want to solve the problem."
"I appreciate his courage - he has got courage and has shown courage for the past six months" since he took power.
"He has shown a deep desire to unify his country," Bush said referring to criticism of the prime minister's failure to do more to put a lid on sectarian violence that has been raging since an attack on a revered Shia shrine in February.
Not offended
The US president's show of support came after US officials insisted on al-Maliki was not offended by a critical White House memo and had not snubbed Bush in Amman on Wednesday when the two had been expected to meet.
Bush said he and al-Maliki agreed in high-stakes talks that Iraq should not be partitioned into separate, semi-autonomous zones.
"The prime minster made clear that splitting his country into parts, as some have suggested is not what the Iraqi people want, and that any partition of Iraq would only lead to an increase in sectarian violence," Bush said after nearly two and a half hours of discussions aimed at stabilising violence-wracked Iraq.
"I agree," he said.
For his part, al-Maliki denied that Iran had any influence over Iraq or any part of the embattled capital Baghdad.
He also said Iraq will never allow any foreign control of his war-wracked country. "We have repeatedly said, and we reaffirm once more, that we will never allow anyone to control any part of Iraq," al-Maliki said, when asked about alleged Iranian interference in Iraq.
"There are [foreign] interferences but any talk about [foreign] control is exaggerated."
Three-way talks cancelled
Original plans for three-way talks were abandoned at the last minute but talks between Bush and al-Maliki went ahead in Jordan.
They met for a working breakfast at the hotel where Bush is staying.
Explanations for the change to the scheduled talks between Bush, al-Maliki and King Abdullah were confusing.
White House officials said the Jordanians and the Iraqis jointly decided three-way talks were not the best use of time as both parties would be meeting the president separately.
Redha Jawad Taqi, a senior aide of Shia politician Abdulaziz al-Hakim, however, said the reason for the change had been because the Iraqis believed Abdullah wanted to broaden the talks to include the Israeli-Palestinian conflict.
At the same time, two senior officials travelling with al-Maliki said the Iraqi prime minister had been reluctant to travel to Jordan in the first place and decided, once in Amman, that he did not want a "third party" involved in talks about subjects specific to the US-Iraqi relations.
Meanwhile, in Iraq 30 lawmakers and five cabinet ministers loyal to anti-American Shia leader Muqtada al-Sadr boycotted parliament and suspended their participation in the national unity government in protest at the meeting.
A statement released by the group said Bush's talks with al-Maliki were a "provocation to the feelings of the Iraqi people and a violation of their constitutional rights".
