US President Donald Trump has labelled his Democrat opponents "hypocrites" after they called for Attorney General Jeff Sessions to resign over his contacts with Russia.

Trump on Friday tweeted a photograph of Senate minority leader Chuck Schumer eating doughnuts with Russian President Vladimir Putin.

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

A second Trump tweet showed House minority leader Nancy Pelosi at a large table across from top Russian officials and called for her to be investigated, too.

On Thursday, Schumer and Pelosi led calls by opposition Democrats in Congress for the resignation of Sessions, who during confirmation hearings in January failed to disclose 2016 meetings with the Russian ambassador to Washington, Sergey Kislyak.

We should start an immediate investigation into @SenSchumer and his ties to Russia and Putin. A total hypocrite! pic.twitter.com/Ik3yqjHzsA — Donald J. Trump (@realDonaldTrump) March 3, 2017

Responding to Trump, Schumer pointed out that the 2003 meeting at a Russian-owned Lukoil gas station in Long Island, New York, was "in full view of press & public".

The New York senator said he would "happily talk" under oath and asked if "you & your team" would do likewise.

The Schumer photo had circulated on pro-Trump websites before being tweeted by the president.

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In the tweet about Pelosi, Trump linked to a 2010 photo in which she and other lawmakers are shown meeting with Russian officials, including then-President Dmitry Medvedev and Ambassador Sergey Kislyak.

Pelosi had initially denied ever meeting Kislyak; her spokeswoman later clarified that they never had a one-on-one meeting.

After Trump's tweet, Pelosi replied that Trump "doesn't know the difference" between an official meeting photographed by the press and a "secret" meeting that Sessions "lied about under oath".

Sessions said on Thursday he would disqualify himself from justice department decisions on investigations related to 2016 presidential campaigns.

The FBI is reportedly probing ties between Russia and the Trump campaign, but the justice department does not routinely acknowledge investigations.

Sessions and the Kremlin denied that there had been any inappropriate contact.

"I never had meetings with Russian operatives or Russian intermediaries about the Trump campaign," Sessions said on Thursday.

In Moscow, a Kremlin spokesman called it "normal practice" for diplomats to meet foreign officials.

Sessions said the ambassador meetings were part of his role as a member of the Senate Armed Services Committee and not linked to his role as an adviser in the Trump campaign.

In his January 10 confirmation hearing, Sessions said: "I did not have communications with the Russians."

Trump's national security adviser, Michael Flynn, resigned last month after it emerged that he had been in contact with Kislyak about US sanctions against Russia.