US President Donald Trump has asked his national security adviser, John Bolton, to invite Russian President Vladimir Putin to Washington in the autumn, the White House has said.

White House Spokeswoman Sarah Sanders said in a tweet that: "President Trump asked John Bolton to invite President Putin to Washington in the fall and those discussions are already under way."

It comes as Mr Trump insisted that the first meeting was a success despite widespread criticism at home and abroad.

He singled out the "Fake News Media" as the real enemy of the people in a series of tweets in which he said Israel, Ukraine and peace in the Middle East would be discussed at the next meeting.

Mr Putin earlier accused forces in the United States of trying to undermine the success of the first summit, but said the two leaders had begun to improve US-Russia ties anyway.

Mr Putin and Mr Trump sat down for their first summit in Helsinki on Monday, an event that sparked a storm of criticism in the US after Mr Trump refused to blame the Russian leader for meddling in the 2016 US election, something Mr Putin denies.

Mr Trump later said he had misspoken and accused "some people" of hating the fact that he got along with Mr Putin.

The White House has been struggling to contain a political outcry and confusion over the summit ever since.

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Mr Putin, speaking to Russian diplomats from around the world assembled in Moscow, said the Helsinki summit had been successful.

"It was successful overall and led to some useful agreements. Of course, let's see how events will develop further," he said, without disclosing the nature of the agreements he referred to.

However, Mr Putin said "powerful" US forces were trying to sabotage what the summit had achieved.

"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."

Those same forces appeared ready to sacrifice hundreds of thousands of US jobs and hurt US business and security while waging their divisive political battle, Mr Putin said.

Mr Trump also hit out at the European Union after it fined Google €4.34 billion in relation to its Android mobile devices and warned he would no longer allow Europe to take "advantage" of the United States.

"I told you so! The European Union just slapped a Five Billion Dollar fine on one of our great companies, Google," Mr Trump tweeted.

"They truly have taken advantage of the U.S., but not for long!" he said.

European Commission President Jean-Claude Juncker is scheduled to meet Mr Trump at the White House next Wednesday to discuss trade and other issues.

Google said it would appeal the EU decision.