WASHINGTON—Turkey is asking the U.S. to provide substantial military support, including airstrikes, transport and logistics, to allow Turkish forces to assume the main responsibility for fighting Islamic State militants in Syria, senior U.S. officials say.

The Turkish requests are so extensive that, if fully met, the American military might be deepening its involvement in Syria instead of reducing it, the officials added. That would frustrate President Trump’s goal of transferring the mission of finishing off Islamic State...