Blair held talks with President Jalal Talabani and Prime Minister Nuri al-Maliki on ways to rebuild security in Iraq amid unrelenting sectarian violence.
As Blair visited, gunmen were reported to have massacred 15 people in an Shi'ite Kurdish village, while the United States military said five more U.S. soldiers had been killed.
At a press conference, Blair said he was not surprised that the Green Zone government headquarters in Baghdad had been bombarded by shells during his visit.
"There are mortar attacks and terrorist attacks happening every day," he said. "That's the reality. The question is 'what are we going to do in the face of those attacks?' Those attacks by a minority of people who want to destroy progress here. The answer is, we don't give in to them. The very purpose of the attacks, the suicide bombs, the mortars aimed in here is so that you [journalists] will carry nothing but that on your news and won't actually talk about the progress that's happening."
Blair maintained that despite "the challenges" in Iraq, "there are real signs of change and progress also."
"I've no doubt at all that Britain will remain steadfast in its support for Iraq, for the Iraqi people, and for the Iraqi government." -- Blair
The prime minister reiterated he had no regrets about his part in the U.S.-led invasion of Iraq. He said he had no doubt London would continue the same policy under his expected successor as prime minister, Gordon Brown.
"I've no doubt at all," he said, "that Britain will remain steadfast in its support for Iraq, for the Iraqi people, and for the Iraqi government as it tries to make sure that it overcomes the threat of terrorism and continues to make progress."
Blair said that "history will judge" whether his support of the U.S.-led invasion and subsequent occupation of Iraq was the right move.
Blair also said Britain could have only a positive relationship with Iraq's neighbor Iran if Tehran supports the democratically elected Iraqi government.
Former U.S. President Jimmy Carter has criticized Blair for what Carter called his "blind" support of the war in Iraq. As Blair visited Baghdad, Carter told the BBC that Blair's backing for U.S. President George W. Bush had been "apparently subservient."
Blair himself understands the matter completely differently. On May 17, he said in Washington that he never had doubts about London's current relationship with the United States.
Blair is due to step down on June 27.