New York: US President Donald Trump has called Turkey's invasion of northern Syria a "bad idea", while distancing himself from the Kurds because they did not help the US in World War II - specifically the invasion of Normandy.

Trump's reaction was far milder than that of senior Republicans in Washington, who blasted the Turkish incursion and redoubled their attacks on the President for withdrawing US troops from the region.

The unusual level of criticism from Trump's political allies comes as he faces an impeachment battle with Democrats in Congress and new polls showing a majority of Americans now support his removal from office.

Turkish President Recep Tayyip Erdogan announced the start of the military action on Twitter on Wednesday local time (Thursday AEDT), saying the aim was to eliminate a "terror corridor" on his country's southern border.