Blair, who was making an unannounced visit before he steps down from office in June, planned to reassure Iraqi Prime Minister Nouri al-Maliki that his departure will not bring an end to Britain's support.
Three mortar rounds or rockets exploded Saturday in the Green Zone, wounding one person, after Blair arrived there for talks with Iraqi leaders. Blair's official spokesman downplayed the incident, saying there was "nothing to suggest anything other than business as usual."
A fourth projectile exploded just outside the Green Zone, U.S. Embassy spokesman Lou Fintor said. Fintor did not say where the blasts occurred and made no mention of Blair's presence.
The blasts occurred about 11:30 a.m., soon after Blair arrived for meetings with al-Maliki and President Jalal Talabani. It was unclear how far the explosions occurred from the meeting site.
Blair arrived in Iraq via Kuwait, following talks in Washington with President Bush on Thursday.
Blair told a Rose Garden news conference that Britain's next leader, current Treasury chief Gordon Brown, would continue to back al-Maliki's government, saying Iraq was a critical battleground in the fight against global terrorism.
"The forces that we are fighting in Iraq — al Qaeda on the one hand, Iranian-backed elements on the other — are the same forces we're fighting everywhere," Blair told reporters.
Talks with al-Maliki and Talabani were to center on speeding up reconciliation between divided communities, British officials said.
Blair's official spokesman, who briefs reporters only on condition of anonymity, said tribal elders and community leaders who may be "connected with people who have committed violence" must be engaged with.
Coalition officials have been cautiously optimistic over evidence that some tribal leaders in Anbar province had ousted al Qaeda-linked insurgents hiding in their communities, Blair's spokesman said.
Britain did not believe in talks with foreign terrorists, he said, but would support moves to bring those whose violence was motivated by "concerns about whether their community will have a place in the new Iraq" into the political sphere.
Blair hopes provincial elections could take place in 2007 and that Sunni groups, who boycotted the last similar poll, would field candidates, his spokesman said.
Britain has almost completed the process of pulling about 1,600 troops out of Iraq, leaving a force of around 5,500 based mainly on the fringes of the southern city of Basra.
Troops levels are likely to fall below 5,000 in late summer, but Blair has said British soldiers will stay in the Basra region until at least 2008 to train local forces, patrol the Iran-Iraq border and secure supply routes.
Prince Harry, third in line to the British throne, will not carry out a planned tour of duty in southern Iraq with his regiment after army chiefs ruled there were specific threats to the young royal's life.
In an emotional resignation speech to members of his Labour party last week, Blair acknowledged violence directed at civilians and coalition troops in Iraq has been "fierce and unrelenting and costly."
A mounting military death toll — 148 British troops have died in Iraq since the start of the 2003 invasion — has led some Britons to call for Brown to speed up the withdrawal of British soldiers and to cool relations with Bush.
Brown said last Sunday that Britain was "a divided country over Iraq," but claimed most citizens — even those opposed to the invasion — accepted that it is in their interests to support al-Maliki's administration.