ISLAMABAD- Pakistani police have arrested 30 suspects in connection with a bombing that killed three American soldiers, three children and a Pakistani paramilitary soldier outside a girls' school, an officer said.

Naeem Khan, duty officer in the police station in the town of Timergara in the northwest where the attack took place, said police suspect the Wednesday bombing was a suicide attack.

We have recovered the engine of the car we suspect was used in the bombing, Khan told Reuters.

Pakistan's Taliban claimed responsibility for the attack and threatened more attacks on Americans.

Forty-five people were wounded in the blast near the Swat Valley, where the government mounted a crackdown nearly a year ago it said had largely cleared out Taliban militants.

We have also found some limbs which we suspect are of the bomber. We have sent these limbs for DNA tests, Khan said.

Pakistan's Taliban have bombed markets, schools and military and police facilities despite major government security offensives that have destroyed some of their bases and U.S. drone aircraft strikes that have killed their leaders.

The three U.S. soldiers were part of a small unit that trains Pakistani Frontier Corps responsible for security in northwestern areas near the Afghan border seen as part of a global militant hub.

They were on their way to attend the opening of a girls' school that had recently been renovated with U.S. humanitarian assistance when the bomb exploded, leaving a crater a few feet away from the school.

(Reporting by Zeeshan Haider; Writing by Michael Georgy)