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US President Donald Trump described a probe into his team's alleged dealings with the Russian government as the "single greatest witch hunt" in US history.

It comes as the former FBI chief Robert Mueller was appointed special counsel to investigate the alleged links.

"This is the single greatest witch hunt of a politician in American history!" Trump wrote on Twitter.

Trump also alleged that former Democrat Secretary of State Hillary Clinton's campaign team and Barack Obama's administration committed "illegal acts".

"With all of the illegal acts that took place in the Clinton campaign & Obama Administration, there was never a special councel [sic] appointed!" he wrote.

Trump has denied any links to Moscow but the appointment of a special counsel poses perhaps the greatest threat to his presidency.

Recently he was accused of attempting to block the investigation by firing FBI chief James Comey and sharing state security secrets with Russian Foreign Minister Sergei Lavrov.

On Wednesday, Trump said that "no politician in history had been treated more unfairly".