The bombing at a bus station came soon after another went off in the centre of Basra, Iraq's main port city, at about 11:00 am (0800 GMT), causing no casualties, Ali al-Maliki said.
No group immediately claimed responsibility, but militants including those linked to Al-Qaeda target civilians, security forces and government employees in a bid to reduce confidence in the government and destabilise the country.
Attacks in Basra are relatively rare compared with other areas of Iraq, especially the centre, west and north.
Violence has decreased from its peak in 2006 and 2007 when sectarian bloodshed raged between Sunni and Shiite Arabs, but 10 years after the US-led invasion, attacks remain common, killing 220 people last month, according to an AFP tally based on security and medical sources.
Britain-based Iraq Body Count (IBC) published a study on Sunday concluding that at least 112,000 civilians were killed in the 10 years since the US-led invasion of Iraq.
It said that, including combatants on all sides of the decade-long conflict as well as yet-undocumented fatalities, the figure could rise as high as 174,000.
"This conflict is not yet history," it said in its report, which put the number of civilian deaths since March 20, 2003 at between 112,017 and 122,438.
"It remains entrenched and pervasive, with a clear beginning but no foreseeable end, and very much a part of the present in Iraq."