The New York Times, citing advisers briefed on the meeting, reported that Donald Trump Jr. attended the meeting.
The New York Times, citing advisers briefed on the meeting, reported that Donald Trump Jr. attended the meeting after being promised "damaging information" about his father's Democratic rival Hillary Clinton -- the latest revelation to surface in the probe over possible collusion between the Trump campaign and Russia.
Trump's eldest son was reportedly joined by the US president's son-in-law Jared Kushner and then-Trump campaign chairman Paul Manafort for the June 2016 meeting in New York with the Kremlin-connected lawyer, the earliest such contact yet reported.
The younger Trump said in a statement to the Times that the lawyer, Natalia Veselnitskaya, "stated that she had information that individuals connected to Russia were funding the Democratic National Committee and supporting Mrs Clinton."
"It quickly became clear that she had no meaningful information," he said, adding that the lawyer then began discussing the adoption of Russian children by American couples under a program Putin had suspended.
The president's son said he gathered that the adoption issue was "the true agenda all along and that the claims of potentially helpful information were a pretext for the meeting."
The report followed a series of early-morning tweets by Trump two days after his first face-to-face talks with his Russian counterpart, in which he said he confronted Putin when they met in Germany over evidence from the intelligence agencies that Moscow interfered in the US election.
"I strongly pressed President Putin twice about Russian meddling in our election," he said of Friday's meeting on the sidelines of the G20 summit in Hamburg. "He vehemently denied it. I've already given my opinion..."
While ruling out easing sanctions so long as the two countries remain at odds over Syria and Ukraine, Trump said it was time for US-Russia relations to move forward, even as members of his own Republican party said he should be mulling new punishments.
Several Republican lawmakers also scoffed at Trump's tweet that he and Putin had talked about the idea of setting up what he called "an impenetrable cyber security unit" to prevent hacking in future elections.
The president later returned to Twitter saying the creation of such a unit was unlikely: "The fact that President Putin and I discussed a Cyber Security unit doesn't mean I think it can happen. It can't."
Trump did say they could work together on some areas, including on Syria, where he said a ceasefire that began on Sunday would "save lives."
"Now it is time to move forward in working constructively with Russia!"
Lindsey Graham, a member of the Senate's armed services committee, said the idea of a joint cyber security unit was "not the dumbest idea I've ever heard, but it's pretty close."
His voice dripping with sarcasm, former presidential candidate John McCain told CBS he was "sure that Vladimir Putin could be of enormous assistance in that effort, since he's doing the hacking."
The US and Russia have issued sharply conflicting accounts of Friday's meeting, with Putin saying on Saturday that Trump had been "satisfied" by his denials of any Russian interference in the election.
Trump has previously equivocated over whether Russia did try to tilt the outcome of the November contest against Clinton in his favor, amid an investigation into whether members of his campaign team actively colluded with Moscow.
So his public assessment that Russia may have meddled in the vote has triggered calls to bring in more sanctions.
"So far they have not paid a single price for that," McCain said.
Moscow has warned that a program of existing sanctions, which were mainly imposed over Russia's annexation of Crimea in Ukraine, threatens their whole relationship.
Asked on Sunday whether new sanctions were in the pipeline, US Treasury Secretary Steve Mnuchin told ABC television: "We have sanctions that are already on the table and we expect to enforce those sanctions."
Mnuchin also insisted that Russia and the US could work together on cyber security: "This is like any other strategic alliance, whether we're doing military exercises with our allies or anything else."
Syria has been a particular source of friction between the two countries, as Russia is a close ally of President Bashar al-Assad.
While saying sanctions were not discussed at the meeting with Putin, Trump indicated that Moscow could not expect any relief "until the Ukrainian & Syrian problems are solved."
But while the brokering of a Syria ceasefire by the two countries -- along with Jordan -- means that one area of tension could be eased, the differences over Ukraine remain stark.
Speaking on a visit to Ukraine, US Secretary of State Rex Tillerson urged Russia to take action to ease the separatist conflict in the country's east, which Kiev and the West believe is being fueled by Moscow.
"It is necessary for Russia to take the first step to de-escalate the situation in eastern Ukraine," Tillerson said as he made his first visit as Washington's top diplomat to Kiev.