WASHINGTON — The White House, pushing hard against criticism in Congress over the deepening air war in Libya, asserted Wednesday that President Obama had the authority to continue the military campaign without Congressional approval because American involvement fell short of full-blown hostilities.

In a 38-page report sent to lawmakers describing and defending the NATO-led operation, the White House said the mission was prying loose Col. Muammar el-Qaddafi’s grip on power.

In contending that the limited American role did not oblige the administration to ask for authorization under the War Powers Resolution, the report asserted that “U.S. operations do not involve sustained fighting or active exchanges of fire with hostile forces, nor do they involve U.S. ground troops.” Still, the White House acknowledged, the operation has cost the Pentagon $716 million in its first two months and will have cost $1.1 billion by September at the current scale of operations.

The report came one day after the House Speaker, John A. Boehner, Republican of Ohio, had sent a letter to Mr. Obama warning him that he appeared to be out of time under the Vietnam-era law that says presidents must terminate a mission 60 or 90 days after notifying Congress that troops have been deployed into hostilities, unless lawmakers authorize the operation to continue.