US President Donald Trump has hit out at the Senate Democratic leader Charles Schumer after a picture emerged of the latter sharing a joke with Russian President Vladimir Putin.

Trump, who tweeted the picture of Schumer and Putin together, called Schumer a hypocrite in response to Democrat demands for an investigation into Trump's own connection with Putin.

Trump wrote on Twitter: "We should start an immediate investigation into ‪@SenSchumer and his ties to Russia and Putin. A total hypocrite!"

The president's ties to Russia and Putin have come under scrutiny, with Democrats demanding a full investigation.

As the pressure increased, US Attorney General Jeff Sessions yesterday removed himself from investigations relating to the Trump campaign team's links to Russian officials after it was revealed that he had met Russian ambassador Sergey Kislyak twice before the presidential election.

Intelligence agencies in the US have said that at the time Russia was attempting to interfere in the election to help Trump win the presidency.

Trump has described Sessions as "an honest man" and said that the Democrats' calling for his head was part of "a total witch hunt".

In a response to Trump's tweet revealing the picture, which was taken in 2003, Schumer tweeted this challenge: