Mr Straw told BBC radio that British forces would be in Iraq “at least for a couple of years”, adding “it could be longer”.
Britain has about 8700 troops in Iraq as part of the US-led occupation force.
The turmoil in the US-occupied nation was further confirmed when US President George W. Bush accused al-Qaeda of carrying out the morning rush hour explosions in Basra that killed 68 people and wounded at least 200.
“They just blew up innocent Iraqis,” he said in Washington.
An extremist group with links to al-Qaeda has claimed responsibility for the Saudi blast that killed at least four people and injured 148.
Addressing “tyrants” in Saudi Arabia, the group, calling itself the Brigade of the Two Holy Mosques in the Arabian Peninsula, warned on a website that the attack on the headquarters of the Saudi security service was “only one punishment technique that we are going to inflict on you”.