US President Donald Trump has informed voters the White House is running 'very well', as he encouraged people not to believe the negative reports about his administration.

The Republican has faced a difficult week following a number of information leaks from the White House, that have caused several problems and resulted in the resignation of Mike Flynn as national security adviser.

The number of leaks has led to several promises from White House press secretary Sean Spicer that he will stamp out the problem, and added to speculation there are serious problems in the Trump's administration.

But in a tweet, the president said all was well, stating: "Don't believe the main stream (fake news) media. The White House is running VERY WELL. I inherited a MESS and am in the process of fixing it."

His comments come just days after he lambasted the media during his first solo press conference, in which he claimed the leaks were real, but the information leaked was "fake news".

Addressing the resignation of Flynn - which came following leaks that revealed he had been in contact with Russia's US ambassador prior to Trump taking office - he said during his press conference: "It's now starting to turn. People giving out illegal classified information.

"I called, as you know, Mexico. It was a very confidential, classified call. All of a sudden it's out there for the world to see. It's supposed to be secret. Same thing with Australia.

"All of a sudden people are finding out exactly what took place. The same thing happened with General Flynn. The leaks are real, but the news is fake because so much of the news is fake," he said.

He added: "The first thing I thought when I saw this was how does the press get this classified information? You know why, because it's an illegal process. And the press should be ashamed of themselves."