BAGHDAD — The American military has offered rewards of up to $200,000 for information leading to the return of three missing American soldiers, an American general said yesterday.

The commander of American troops south of Baghdad, Major General Rick Lynch, said the offer was made on 50,000 leaflets distributed in the area where the troops disappeared after a predawn ambush Saturday in which four American troops and an Iraq soldier were killed. An Al Qaeda front group — the Islamic State of Iraq — has said it captured the soldiers.

Word of the reward was also broadcast over loudspeakers as part of a search involving 4,000 American troops and 2,000 Iraqis, General Lynch told the Associated Press. Troops have pursued 143 intelligence leads, staged eight air assault operations, and established blocking positions to keep those behind the abductions from fleeing with their captives.

“We’ve done so much as to drain canals after a report that the bodies were in a canal,” he said. “So we’re leaving no stone unturned.”

General Lynch said he was optimistic that the three soldiers would be found alive and the search remained focused on the area where they went missing. “We’re pursuing all intelligence,” he said. “Some of those leads tell us that the soldiers have been taken out of the area but the majority tell us that they’re still in the area.”