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Donald Trump has said he has complete power to pardon himself, as a probe into his administration's alleged links with Russia continue to hang over the US president.

In a series of bizarre tweets, the president attacked the media and Hilary Clinton and said that a probe into alleged collusion with Russia was sparked by leaked emails.

"While all agree the U. S. President has the complete power to pardon, why think of that when only crime so far is LEAKS against us. FAKE NEWS," he wrote on Twitter.

"So many people are asking why isn't the A.G. or Special Council looking at the many Hillary Clinton or Comey crimes. 33,000 e-mails deleted?" he wrote in another.

Trump could be referring to a The Washington Post claim this week that his legal team had been investigating whether he could be use his powers as president to pardon himself, family members or aides.

It comes as a probe into the Trump team's alleged collusion with Russia during last year's presidential campaign.

The Post claims that Russia's US ambassador had overheard spy agencies saying they had spoken to Trump's Attorney General Jeff Sessions - then senator - about the controversial campaign.

Sessions initially failed to disclose these meetings and the Post said the former senator had met Ambassador Sergey Kislyak and discussed the election campaign.

Special Counsel Robert Mueller is looking into possible links between Trump and Russia, and investigating Moscow's possible interference in the presidential race which saw Hilary Clinton lose to Trump.