After the March 20 phone call - in which Trump congratulated Putin for a re-election victory in a vote widely criticized as not free and fair - Trump told reporters that the two leaders had discussed a possible meeting to discuss Syria, Ukraine, North Korea and "the arms race." He did not mention any meeting venues at that time.
White House press secretary Sarah Huckabee Sanders said Monday that "a number of potential venues, including the White House," were discussed.
A Kremlin aide, Yury Ushakov, disclosed the White House invitation in comments to Russian journalists Monday.
"If everything will be all right, I hope that the Americans will not back away from their own proposal to discuss the possibility of holding a summit," Ushakov said, according to the state news agency RIA Novosti. "When our presidents spoke on the phone, it was Trump who proposed holding the first meeting in Washington, in the White House."
He added that no preparations for such a meeting have been made, according to Russian news agencies.
If a White House visit did come together, it would be Putin's first since 2005 - when Moscow and the West were on better terms.
Those relations have been in a free fall since the nerve-agent poisoning of a former Russian double agent and his daughter in Britain on March 4. British authorities blamed the attack on Russia. Trump was slow to back their assessment, but the United States on March 26 joined countries in Europe and elsewhere in retaliatory expulsions of Russian diplomats.
The Kremlin denies it had anything to do with the nerve-agent attack and has ordered tit-for-tat expulsions. The former spy, Sergei Skripal, and his daughter, Yulia, remain hospitalized.
The added detail that Trump floated a White House meeting with Putin renews debate over a presidential phone call that came in the midst of that political storm and drew broad criticism last month.
In the March 20 call, Trump congratulated Putin on his re-election to a fourth term two days earlier and did not raise the nerve-agent attack. His national security advisers had urged him to condemn the Skripal poisoning and included an instruction in his briefing book that said, "DO NOT CONGRATULATE," officials familiar with the call told The Washington Post afterward.
Many international observers described Putin's re-election victory as a sham. Sen. John McCain, R-Ariz., said Trump's congratulations for Putin "insulted every Russian citizen who was denied the right to vote in a free and fair election."
Leon Aron, a resident scholar and the director of Russian studies at the American Enterprise Institute, said he was stunned by reports that Trump so willingly suggested a White House meeting.
"Are you kidding me? Are you kidding me?" Aron said. "It's really mind-boggling. I'm usually not this emotional."
Such summits are "a very precious commodity" for Russian presidents, boosting their popularity at home, and should only be offered as a reward, Aron said. He noted that in addition to the spy poisoning episode, Putin last month bragged about the strength of his country's nuclear weapons in a nationalistic speech that was accompanied by an animated video depicting warheads aimed at Florida. The Kremlin also scheduled the presidential election to coincide with the anniversary of Russia's formal annexation of Crimea.
If Trump meets with Putin as an equal given these events, Aron said, he is sending the message that it's okay to "kill more people, seize more territory."
Michael McFaul, a Stanford University professor who was the U.S. ambassador to Russia from 2012 to 2014, said Trump should only meet with Putin if "such a summit would put pressure on both countries to achieve some tangible outcome in America's national interest."
"Right now, it's very hard to see what those might be," McFaul said. "It's not even clear to me that diplomats in our two countries are working together on any issue of mutual interest at this time. Especially given Putin's recent behavior in the world, a summit that just gives Putin a smiley photo op in the Oval Office does not serve American national interests."
The White House on Monday sought to play down the meeting proposal.
"As the president himself confirmed on March 20, hours after his last call with President Putin, the two had discussed a bilateral meeting in the 'not-too-distant future' at a number of potential venues, including the White House," Sanders said in a statement after Ushakov's comments. "We have nothing further to add at this time."
Given the worsening environment, Ushakov said Monday, "it is, of course, difficult to discuss the possibility of holding a summit," Russia's Interfax news agency reported.
"I hope that the situation will allow us to discuss this issue," the Kremlin aide added, referring to the planning for a Trump-Putin summit, according to Interfax. "We believe that it is rather important and necessary for both countries and for the entire international community."
Since Trump became president, the two have met at the Group of 20 summit in Germany in July and, briefly, at the Asia-Pacific Economic Cooperation summit in Vietnam in November.
But a full-blown bilateral meeting has proved elusive, in part because of political head winds in Washington, fanned by the investigations into Russian interference in the 2016 U.S. election and into possible collusion with the Trump campaign.
For Putin, a sit-down with Trump at 1600 Pennsylvania Ave. would represent "a dream come true," said Vladimir Frolov, an independent foreign policy analyst in Moscow.
"I think his entire strategy now is to get into a long private meeting with Trump and use his intel charms on him," Frolov said of Putin, a former KGB agent. He added, however, that the Kremlin's decision to disclose the detail about the White House invitation may also have been meant to embarrass Trump, which could provoke an adverse reaction from the U.S. president.
Putin last visited the White House for a 2005 meeting with President George W. Bush, who afterward described Russia as a "strong ally" in the war on terrorism. Dmitry Medvedev, during his term as Russian president, held White House talks with President Barack Obama in 2010, but Putin has not made another White House visit since he returned to the presidency in 2012.
In 2013, Obama canceled a planned Moscow summit with Putin after Russia took in Edward Snowden, the National Security Agency leaker facing espionage charges in the United States.
A White House visit, despite the deterioration in ties between the United States and Russia since Putin's annexation of Crimea in 2014, would probably be depicted in Russia as a victory for Putin, who has cast himself as a leader rebuilding the country's global influence while reasserting Russian interests.
The Russian news media has cast the criticism of Trump as too friendly with Putin as evidence of the U.S. establishment seeking to undermine its president's efforts to pursue a sober, fair-minded Russia policy.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)