Washington(CNN) President Donald Trump hopes to welcome Russian President Vladimir Putin in Washington this fall, White House press secretary Sarah Sanders said in a statement Thursday.

"President Trump asked (national security adviser John Bolton) to invite President Putin to Washington in the fall and those discussions are already underway," Sanders tweeted Thursday, hours after Trump tweeted he is "looking forward" to meeting again with Putin to "begin implementing" issues they discussed during their summit earlier this week.

The invitation was extended to Putin by Bolton earlier on Thursday, according to a National Security Council spokesman.

The pair of tweets were the latest indication that Trump is doubling down on his Russian rapprochement strategy even as his approach to Putin continues to draw bipartisan criticism and questions abound as to what Trump and Putin agreed to during their first meeting.

The Director of National Intelligence Dan Coats said he still does not know what Trump and Putin discussed on Monday and was caught off-guard during an interview Thursday by news that Trump and Putin were planning a second meeting in Washington this fall.

"Say that again?" Coats offered. "That's gonna be special."

White House officials have not explained why Coats was not informed about the invitation in advance.

The preparations for a second Trump-Putin meeting -- and in Washington no less -- were the latest twist in Trump's winding road back from Helsinki. Since he refused to back the US intelligence community's assessment of Russian interference in 2016, Trump has alternated between trying to quell the political uproar he ignited and seeking to avoid backing down from his handling of the summit.

Trump later said he misspoke when he suggested he didn't believe Russia was behind a cyber influence campaign in 2016, but he has not acknowledged that he repeatedly put the US intelligence community's assessment and Putin's denials on the same footing -- even giving added credence to Putin's denial.

Instead, Trump has used his clean-up remarks to again insist that there was "no collusion" between his campaign and Moscow, while also insisting that it "could be other people also" who interfered in the 2016 election.

And while he later acknowledged in an interview with CBS News that Putin was responsible for the effort to undermine the election, he only attributed that responsibility to Putin being "in charge of the country." The New York Times later reported, and the former Director of National Intelligence James Clapper confirmed to CNN, that Trump was briefed on specific US intelligence indicating that Putin personally ordered the 2016 Russian influence campaign.

Trump on Wednesday again reignited the controversy when he replied "no" when asked if Russia is still targeting the United States, directly contradicting the current Director of National Intelligence Dan Coats. White House press secretary Sarah Sanders claimed later in the day that Trump was saying "no" to answering additional questions.

On Thursday, Trump offered fresh remarks, claiming to CNBC he has been "far tougher on Russia than any president in many, many years" and warning that he would be Putin's "worst enemy" if their diplomatic engagement does not work out.

News of a second Trump-Putin summit came soon after the Senate voted unanimously to rebuke Putin's attempt to convince Trump to hand over current and former American officials for questioning -- an offer Trump had previously called "incredible. Moments before the vote, the White House rebuked its openness to Putin's offer.

Trump on Thursday also accused the news media -- which he again dubbed the "enemy of the people" -- of distorting the summit and pining for a confrontation between the US and Russia, blaming reporters even as much of the coverage this week has focused on Republicans' condemnations.

In a series of tweets Thursday morning, Trump argued his summit with Putin "was a great success."

"The Summit with Russia was a great success, except with the real enemy of the people, the Fake News Media," Trump said. "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."

"There are many answers, some easy and some hard, to these problems...but they can ALL be solved!" Trump tweeted.

Putin has signaled in the wake of his summit with Trump that he and the US President reached several agreements, but neither Trump nor the White House have confirmed any substantive agreements between the two countries.

Trump's "enemy of the people" attack on Thursday marked the second time Trump has emerged from a summit with a dictator who has restricted press freedoms and subsequently attacked the news media as an "enemy."

"Our Country's biggest enemy is the Fake News so easily promulgated by fools!" Trump tweeted last month after he drew heat for overplaying the outcome of his summit with North Korean leader Kim Jong Un.