Mexican President Enrique Pena Nieto said on Monday he had not recently spoken to Donald Trump on the phone, after the US leader boasted his counterpart had called him to praise his border policy.

Mr Trump made the comments as he presented his new chief of staff, former Homeland Security secretary John Kelly, who is tasked with restoring order to a White House beset by scandal, infighting and legislative defeats.

"At Homeland, what he has done has been nothing short of miraculous," Mr Trump said of Mr Kelly.

"As you know, the border was a tremendous problem and they're close to 80 percent stoppage. And even the president of Mexico called me - they said their southern border, very few people are coming because they know they're not going to get through our border, which is the ultimate compliment."