The two CBS network employees were kidnapped from a hotel in Basra on Monday.
“She fled and the soldiers chased her. She ran into an electrical shop where she triggered her vest.”
It was the deadliest attacks in the city since April.
The blast comes amid statements by a US military spokesman that attacks across the country have dropped.
Rear-Admiral Gregory Smith said: “A year ago, there were an average of 205 terrorist attacks each day across Iraq. Last month, we had tracked 82 – a decrease of over 60 per cent.”
This week marks the first anniversary of a so-called surge, where up to 30,000 US troops were deployed to Iraq, aiming to bring down the level of violence.
In other news, the US and Iraq are to begin negotiations on a security agreement to replace a UN mandate for foreign troops, set to expire at the end of this year.
On a visit to Najaf, Ryan Crocker, the US ambassador, said that the Bush administration will not insist on long-term military bases in Iraq.
He said: “I can say directly there is no American demand to set up American long-term bases in Iraq.
“Also there is no Iraqi demand in this connection.”