WASHINGTON—The Trump administration on Friday invoked a rarely used provision of American arms control laws to sidestep Congress and authorize billions of dollars in weapons sales to Middle East allies, angering U.S. lawmakers who characterized the decision as an abuse of power.

Citing concerns about Iran, U.S. officials notified Congress that the administration is declaring an emergency under arms control laws so it can rush through the weapons sales to Saudi Arabia and the United Arab Emirates, two key allies in Washington’s...