New York: US President Donald Trump, facing intense criticism from Republican allies over his decision to pull American troops out of northern Syria, has vowed to "totally destroy and obliterate" Turkey's economy if the country behaves badly in the region.

Senior Republicans lashed out at Trump's decision to allow Turkey to invade north-eastern Syria, saying it could expose Kurds in the area to ethnic cleansing and make America more vulnerable to a September 11-style terrorist attack.

The Trump administration announced the troop withdrawal in a late-night press release on Sunday local time (Monday AEDT), catching Washington's foreign policy community by surprise.

The area includes a camp that houses more than 70,000 people, including 20 Australian women and 46 children.