US President Donald Trump has asked his top national security adviser to invite Russian President Vladimir Putin to Washington for a second summit this year.

White House press secretary Sarah Huckabee Sanders confirmed Mr Trump had approached John Bolton with the request in a media briefing Friday morning (AEST).

Despite continued outrage over Mr Trump’s just-completed Helsinki summit with the Russian leader, Ms Sanders said “discussions are already underway” for a meeting between the two presidents.

While the summit would presumably take place at the White House, Ms Sanders would not elaborate on where Mr Trump and Mr Putin would meet.

In a tweet about Mr Putin overnight, Mr Trump said: “I look forward to our second meeting.”

Mr Trump, who has struggled to quiet an uproar over his failure to confront Mr Putin over Russia’s meddling in the 2016 US election at their summit in Helsinki, blamed the media for negative perceptions of their talks.

“The Summit with Russia was a great success, except with the real enemy of the people, the Fake News Media,” Mr Trump, who was accused of treason by a former CIA boss after the Helsinki summit, wrote on Twitter.

“I look forward to our second meeting so that we can start implementing some of the many things discussed, including stopping terrorism, security for Israel, nuclear proliferation, cyber attacks, trade, Ukraine, Middle East peace, North Korea and more,” the President said.

The Summit with Russia was a great success, except with the real enemy of the people, the Fake News Media. I look forward to our second meeting so that we can start implementing some of the many things discussed, including stopping terrorism, security for Israel, nuclear……..

— Donald J. Trump (@realDonaldTrump) July 19, 2018

….proliferation, cyber attacks, trade, Ukraine, Middle East peace, North Korea and more. There are many answers, some easy and some hard, to these problems…but they can ALL be solved!

— Donald J. Trump (@realDonaldTrump) July 19, 2018

US intelligence agencies last year announced their conclusion that Russia carried out a campaign of hacking and propaganda targeting the 2016 US election in an attempt to sow discord, disparage Democratic candidate Hillary Clinton and aid Mr Trump’s candidacy. Mr Putin has denied any such meddling.

US Director of National Intelligence Dan Coats and FBI Director Christopher Wray publicly reaffirmed their confidence in the findings after the Helsinki meeting.

Mr Trump’s invitation comes after days of confusion as the US President appeared several times assert Mr Putin was not involved with the hacking, before telling CBS on Thursday held the Russian President personally responsible.

Mr Putin overnight blamed “powerful” US forces for attempting to sabotage the talks.

“It was successful overall and led to some useful agreements. Of course, let’s see how events will develop further,” Mr Putin said of the Summit at a meeting of  Russian diplomats in Moscow.

The Russian leader did not disclose the nature of the agreements to which he referred.

“We see that there are forces in the United States that are prepared to casually sacrifice Russian-US relations, to sacrifice them for their ambitions in an internal political battle in the United States,” Mr Putin said.

US prosecutors have offered mounting evidence concerning Russian election meddling. Special Counsel Robert Mueller secured an indictment last Friday charging 12 Russian intelligence officers with hacking Democratic computer networks in 2016 as part of a wide-ranging conspiracy involving sophisticated hacking and staged releases of documents.

-with agencies