Washington (AFP) - US President Donald Trump, under fire over his Helsinki summit with Vladimir Putin, doubled down Thursday by saying he looks forward to meeting the Russian leader again -- with talks already underway for a visit to Washington in the fall.

Trump has come in for bipartisan criticism for what many saw as his unsettling embrace of the Russian strongman this week -- and his seeming disavowal of his own intelligence agencies and their assessment that Moscow meddled in the 2016 election.

The backlash has thrust Trump onto the defensive, leading to days of conflicting statements from both the president and the White House.

But Trump has largely shrugged off the criticism and took aim at the "fake news media" Thursday for failing to recognize his achievements.

"The Summit with Russia was a great success, except with the real enemy of the people, the Fake News Media," Trump said on Twitter. "The Fake News Media wants so badly to see a major confrontation with Russia, even a confrontation that could lead to war."

Meanwhile, Secretary of State Mike Pompeo said Trump's goal was to "redirect" two countries "that'd been on a bad path."

"There's been a lot of heat and very little light following that press conference," he told Catholic television network EWTN.

"I watched the president's interaction with President Putin after their one-on-one meeting ... The President was aiming towards creating a channel for communication and dialogue, and he achieved that," he said, adding he would be "very surprised" if a transcript from the meeting was released.

In an interview with CNBC television, Trump said "getting along with President Putin, getting along with Russia's a positive, not a negative.

"Now with that being said if it doesn't work out I'll be the worst enemy he's ever had," he said of Putin.

"I look forward to our second meeting so that we can start implementing some of the many things discussed," Trump said.

White House spokeswoman Sarah Sanders said that meeting may come this fall.

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"President Trump asked (National Security Advisor John Bolton) to invite President Putin to Washington in the fall and those discussions are already underway," Sanders tweeted.

The invitation came as an apparent surprise to the Director of National Intelligence Dan Coats when he was told about it during a live interview at the Aspen Security Forum in Aspen, Colorado.

"Say that again?" Coats asked the interviewer.

"OK. That's going to be special," he said, laughing.

- 'I don't know what happened' -

Coats also said that three days after Trump met with Putin he does not know what the two men discussed.

"I don't know what happened in that meeting," he said.

The two leaders held two hours of closed-door talks with no one else present but the interpreters.

"If he had asked me how that ought to be conducted, I would have suggested a different way," Coats said.

Trump on Thursday listed the topics discussed as "stopping terrorism, security for Israel, nuclear proliferation, cyber attacks, trade, Ukraine, Middle East peace, North Korea and more."

The top Senate Democrat, Chuck Schumer, had a scathing reaction to news that Trump planned to invite Putin to Washington.

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

The US upper chamber issued a sharp rebuke to Trump earlier in the day, voting 98-0 to oppose any move by his administration to make US officials available for questioning by Russian government officials.

Asked in Helsinki whether he would extradite 12 Russian intelligence agents indicted in the United States for hacking Democratic Party computers, Putin said he could meet the US government "halfway."

Putin said he would permit the 12 to be questioned inside Russia if the United States allowed Russia to question former US envoy to Russia Michael McFaul and 11 others in Moscow's case against billionaire investor and human rights activist William Browder, the driving force behind Magnitsky Act sanctions on Russian officials passed by the US Congress.

Trump initially called it an "incredible offer," but McFaul and others expressed outrage and the White House -- just minutes before the Senate vote -- made clear a deal with Putin was not in the cards.

"It is a proposal that was made in sincerity by President Putin, but President Trump disagrees with it," Sanders said.

- 'Misjudging Putin' -

The indictments of the 12 Russians were issued by special counsel Robert Mueller, who is investigating possible collusion between Trump's campaign and Russia.

According to opinion polls published Thursday, a large majority of Americans disapproved of Trump's handling of the summit -- but members of his party approved by a wide margin.

While just one third of Americans approved of Trump's handling of the Putin summit, that number rose to 68 percent among Republicans, according to a CBS poll.

Among Republicans expressing concern was Senator Lindsey Graham, a prominent voice on foreign policy.

Trump wasn't "prepared as well as he should have been" for the meeting, Graham said, adding that it is "imperative that he understand that he is misjudging Putin."

In Moscow, Putin slammed Trump's domestic opponents as "pathetic, worthless people" who were "ready to sacrifice Russian-American relations for their own ambitions."