US President Donald Trump, his administration under siege for contacts with Russian officials, is calling for "an immediate investigation" into Senate Minority Leader Chuck Schumer and House Minority Leader Nancy Pelosi's own ties to Russia.

Trump tweeted a photo Friday of Schumer meeting with Putin in New York in 2003.

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

The president called for a probe into Schumer's "ties to Russia and Putin" and called the New York senator "A total hypocrite!"

Schumer responded on Twitter a short time later writing that he would "happily talk" under oath about his meeting with Putin, which took place "in full view of press and public."

He then challenged Trump to do the same.

Happily talk re: my contact w Mr. Putin & his associates, took place in '03 in full view of press & public under oath. Would you &your team? https://t.co/yXgw3U8tmQ

— Chuck Schumer (@SenSchumer) March 3, 2017

Trump also tweeted he wants "a second investigation, after Schumer" of Nancy Pelosi "for her close ties to Russia, and lying about it".

I hereby demand a second investigation, after Schumer, of Pelosi for her close ties to Russia, and lying about it. https://t.co/qCDljfF3wN

— Donald J. Trump (@realDonaldTrump) March 3, 2017

Pelosi responded by saying the president "doesn't know the difference" between an official meeting photographed by the press, and a closed secret meeting that his Attorney General, Jeff Sessions, lied about under oath.

.@realDonaldTrump doesn't know difference between official mtg photographed by press & closed secret mtg his AG lied about under oath. https://t.co/YRFCuJkjLA

— Nancy Pelosi (@NancyPelosi) March 3, 2017

Trump's tweets come a day after Jeff Sessions came under scrutiny for his two meetings with a Russian ambassador.