The British leader arrived in Iraq via Kuwait, following talks in Washington with President George Bush on Thursday.
Blair, whose premiership has been tainted by his unpopular decision to join the 2003 invasion of Iraq, told a news conference that Gordon Brown, his successor, would continue to back al-Maliki's government.
He said that 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 said.
'A divided country'
Britain has nearly 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.
Troop levels are likely to fall below 5,000 later in the year, 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.
A mounting military death toll, with 148 British troops having now died in Iraq since 2003, has led some people 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.