(Adds details) BAGHDAD, April 1 (Reuters) - Six U.S. soldiers were killed in roadside bombings southwest of Baghdad over the weekend, marking one of the deadliest periods for American troops since a new security crackdown was launched in the Iraqi capital. The U.S. military said in a statement on Sunday that two soldiers were killed by an explosion during a patrol on Saturday. Four more were killed when another roadside bomb detonated on Sunday near a unit responding to the first attack. A U.S. military spokeswoman said the first attack happened late on Saturday, and that the second unit had responded early on Sunday. The statement did not say precisely where the attack took place, although it said the soldiers killed on Saturday were part of the force assigned to Baghdad. The spokeswoman said she had no information on the location nor whether insurgents might have been waiting for soldiers to respond to the first strike. U.S. and Iraqi forces began a major new offensive against militants in Baghdad in the middle of February, seen as a last ditch attempt to halt the country's plunge into civil war. About half of nearly 30,000 additional U.S. troops being sent to Iraq have now been deployed, a senior U.S. military official said on Sunday. Most will be stationed in Baghdad.