The encounter occurred more than midway through the lengthy dinner, when Mr. Trump left his seat and approached Mr. Putin, who had been seated next to his wife, first lady Melania Trump.
In a statement, a White House official on Tuesday described the meeting as routine and brief, and explained the lack of an American translator by noting that the president was accompanied by a Japanese interpreter who did not speak Russian. The official, who spoke on condition of anonymity, said that any insinuation that the White House has tried to hide the encounter was false.
A second White House official confirmed that the meeting had occurred but did not offer any details, and insisted on anonymity because the discussion was private.
Russia specialists said such an encounter — even on an informal basis at a social event — raised red flags because of its length, which suggests a substantive exchange, and the fact that there was no American interpreter, note taker or national security or foreign policy aide present.
“We’re all going to be wondering what was said, and that’s where it’s unfortunate that there was no U.S. interpreter, because there is no independent American account of what happened,” Stephen Pifer, a former ambassador to Ukraine who also specializes Russia and nuclear arms control.
“If I was in the Kremlin, my recommendation to Putin would be, ‘See if you can get this guy alone,’ and that’s what it sounds like he was able to do,” added Mr. Pifer, a senior fellow at the Brookings Institution in Washington.
The new revelation comes as the Trump administration struggles to improve its relationship with Russia while under pressure from multiple investigations into possible ties between the American president’s campaign and Moscow. Those inquiries have made what normally would be seen as an attempt at diplomacy between world leaders politically toxic.
The evening after Mr. Trump’s two meetings with Mr. Putin — the first lasting 135 minutes and the later, hourlong dinner conversation — the American president returned to Washington. On the Air Force One flight back, his top advisers were helping to draft a statement Mr. Trump approved about a meeting his son, Donald Trump Jr., attended last year with a Kremlin-connected lawyer who was promising damaging information on Hillary Clinton as part of a Russian government attempt to help the Trump campaign.
“We have the worst relationship as a country right now with Russia than we have in decades, and yet we have these two leaders that, for reasons that do not make sense and have not been explained to anyone’s satisfaction, are hellbent on adoring each other,” Mr. Bremmer said. “You can take everything that’s been given to us, and it doesn’t add up.”
On Tuesday, the Kremlin intensified its demands for that the Trump administration return two compounds in the United States that the Obama administration seized from Russia last fall in retaliation for the election meddling. After meeting with Thomas A. Shannon, the under secretary of state for political affairs, Sergei Ryabkov, Russia’s deputy foreign minister, said he had warned the Americans that there must be an “unconditional return” of the property or Moscow would retaliate.
The State Department said no such agreement was in the offing.
“These deals, so to speak, are going to take some time,” Heather Nauert, the State Department spokeswoman, told reporters on Tuesday. “Nothing is coming together anytime soon.”
Mr. Trump announced on Tuesday night that he planned to nominate Jon M. Huntsman Jr., a former envoy to China and Singapore, as his ambassador to Russia. Mr. Huntsman’s nomination has been expected for months, but the multiple investigations into Mr. Trump’s campaign, and whether it colluded with Russia, are likely to figure prominently in his confirmation hearing.