Donald Trump responded to a report detailing what was said to be his frustration with laws.

President Donald Trump on Wednesday denied a US media report that he proposed extreme measures, including alligator-filled trenches, to stop migrants on the Mexican border.

"The press is trying to sell the fact that I wanted a Moot stuffed with alligators and snakes, with an electrified fence and sharp spikes on top, at our Southern Border," Trump tweeted, later correcting the spelling to read "Moat."

"I may be tough on Border Security, but not that tough. The press has gone Crazy. Fake News!" Trump wrote.

He was responding to a New York Times report detailing what was said to be Trump's frustration with laws restricting what he can do to stop migrants.

Trump, the Times reported, discussed using potentially deadly reptiles and also spiked fences. He reportedly suggested allowing soldiers to shoot illegal border crossers in the legs after being told it was not permitted to use deadly force.

Trump has made a clampdown on both illegal and legal immigration one of the keystones of his nationalist "America first" presidency.

Undocumented crossings of the Mexican border have dropped sharply.