Media playback is unsupported on your device Media caption "That's going to be special" - US Director of National Intelligence Dan Coats learns of the Putin visit while at an event

President Donald Trump has invited Russian leader Vladimir Putin to visit the US, in a move that drew startled laughter from a US intelligence chief.

"That's going to be special!" said Director of National Intelligence Dan Coats, when he was told about the invitation during a live interview.

The political fallout is continuing from Mr Trump's first summit with Mr Putin in Finland on Monday.

Democrats are demanding the notes from the two leaders' private talks.

"Until we know what happened at that two-hour meeting in Helsinki, the president should have no more one-on-one interactions with Putin," said Senate Democratic leader, Chuck Schumer, in a statement. "In the United States, in Russia, or anywhere else."

The Republican president's 18 months in office have been dogged by investigations into whether any of his aides colluded with alleged Russian attempts to sway the 2016 election in his favour. Mr Trump and Mr Putin have poured scorn on the claims.

In a CNBC interview televised on Friday, Mr Trump said he and Mr Putin "get along well", even if they did not always see eye to eye.

"It wasn't always conciliatory in that meeting," Mr Trump said. "We discussed lots of great things for both countries, frankly."

He did not offer further details.

Mr Trump also vowed to be the Russian leader's "worst nightmare" if their relationship ever turns sour, and said former President Barack Obama had been Mr Putin's "total patsy".

Trump prepares a sequel

By Anthony Zurcher, BBC News, Washington

Donald Trump has tweeted that the summit with Mr Putin was a "great success" and people at "higher ends of intelligence" loved his Helsinki news conference. As if to underline that point, plans are already under way for a sequel - this time in Washington DC.

Never mind that the White House has spent three days trying to clean up the political fallout from the summit amid bipartisan criticism, or that the special counsel investigation into Russian meddling in 2016 continues apace.

Media playback is unsupported on your device Media caption Trump says he "misspoke" at Putin summit, but is it too late? Anthony Zurcher explains

Mr Trump may have been encouraged by recent opinion polling showing that while the public at large is uneasy with Mr Trump's Russia policies, his Republican base - by a sizeable majority - is fine with his performance.

The president campaigned on closer ties with Russia, a goal that had been thwarted during his first year in office. With his base still behind him, Mr Trump appears ready to press on with his efforts.

What do we know of the plan for a Putin visit?

Mr Putin, in power in Russia since 2000, last visited the US in 2015, when he met President Barack Obama, Mr Trump's predecessor, on the sidelines of the UN General Assembly in New York to discuss the conflicts in Ukraine and Syria.

Image copyright AFP Image caption Mr Putin said he would meet the US "halfway" over access to indictees

On Thursday, White House press secretary Sarah Sanders tweeted that discussions about a visit by Mr Putin to Washington DC this autumn were already under way.

Russia's ambassador to Washington, Anatoly Antonov, could not confirm whether an invitation had already been issued.

He told the BBC: "The problem is there's so much talk today, so much fake news, so much distortion, about what happened at this summit.

"Such negativity for some reason - I don't understand why the Western media think it's bad that two presidents are meeting. What's bad about it?"

Has US intelligence chief 'gone rogue'?

The announcement of a second summit appeared to come as a surprise to Mr Trump's director of national intelligence.

"Say that again," Mr Coats said when an NBC News presenter broke the news to him during a live interview at the Aspen Security Forum in Colorado.

He said he did not yet know what Mr Trump and Mr Putin had discussed during their meeting, at which only the pair and their interpreters were present.

The White House is said to be furious about the director of national intelligence's remarks.

"Coats has gone rogue," one senior official told the Washington Post.

What was Putin's 'incredible offer'?

At the post-summit news conference in Helsinki, Mr Putin offered access to 12 Russians indicted in absentia by the US authorities for allegedly hacking Democratic Party computers, on condition Moscow authorities could question 12 Americans over other matters.

Mr Trump first praised the suggestion as an "incredible offer", but White House press secretary Sarah Sanders later said the president disagreed with it.

No extradition treaty exists between the two countries.

Mr Putin singled out US-born financier Bill Browder, accusing him of massive tax fraud, which he denies.

Mr Browder was instrumental in the US imposing sanctions in 2012 on top Russian officials accused of corruption in the Magnitsky affair.

"I'm thankful that Donald Trump has no intention of handing me over to Vladimir Putin to have me killed in a Russian prison," Mr Browder told the BBC on Thursday.

One of the other Americans on Russia's list was a former US ambassador to Moscow, Michael McFaul.

Media playback is unsupported on your device Media caption Russian ambassadors react to Trump remarks at Helsinki summit

The idea of allowing Russia to quiz US citizens sparked outrage and the US Senate voted 98-0 against it. Secretary of State Mike Pompeo said it was "not going to happen".

Mr McFaul tweeted his gratitude to senators.