Here are some key quotes from their meeting.
PRESIDENT BUSH ON IRAQ'S FUTURE
"Prime Minister Maliki and I just had a very productive meeting. This is the third time we've met since he took office six months ago. And with each meeting I'm coming to know him better. He is a strong leader.
"The prime minister 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. I agree.
"In the long term, security in Iraq requires reconciliation among Iraq's different ethnic and religious communities, something the overwhelming majority of Iraqis want."
PRESIDENT BUSH ON US TROOPS IN IRAQ
"So we'll be in Iraq until the job is complete, at the request of a sovereign government elected by the people. I know there's a lot of speculation that these reports in Washington mean there's going to be some kind of graceful exit, out of Iraq.
"We're going to stay in Iraq to get the job done, so long as the government wants us there."
PM MALIKI ON IRAQI FORCES
"We have agreed and we were clear on the need to speed up the transfer of security responsibilities to the Iraqi forces.
"I believe that the Iraqi security forces are capable enough of protecting the country and its citizens against those who seek to undermine their safety."
PM MALIKI ON IRAQI SOVEREIGNTY
"Iraq is for Iraqis. Its frontiers are defended and we will not allow them to be violated or let people interfere in our internal affairs."
PRESIDENT BUSH ON PM MALIKI
"One of his frustrations with me is that he believes that we've been slow about giving him the tools necessary to protect the Iraqi people....
"The first thing that gives me confidence is that he wants responsibility....
"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'."
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