“There was a couples-only social dinner at the G-20. Toward the end, the president spoke to Putin at the dinner,” Efe quoted National Security Council spokesman Michael Anton as saying.
“No staff or Cabinet were at the dinner at all, for any of the countries.”
The dinner took place hours after Trump and Putin met formally for more than two hours on the sidelines of the conference in the German city.
US Secretary of State Rex Tillerson and Russian Foreign Minister Sergei Lavrov were present for the earlier discussion.
Trump and Putin were seated at opposite ends of the table for the dinner, but the American leader left his spot and sat next to the Russian.
The two presidents spoke for around an hour, accompanied only by Putin’s translator.
Ian Bremmer, president of the US-based Eurasia Group, was the first to disclose the second meeting between Trump and Putin.
In a newsletter to clients, Bremer said he learned of the discussion from two people who were at the dinner.
During the initial session in Hamburg, Trump confronted Putin about allegations of Russian meddling in the 2016 election, prompting the Kremlin chief to repeat his previous denials of any interference.
Earlier Tuesday, the eighth person who took part in a June 2016 between now-President Trump’s oldest son and a Russian lawyer said to have damaging information about Hillary Clinton was revealed to be a US-based representative of a Russian real estate firm.
Ike Kaveladze, a naturalised US citizen, is vice president of the Crocus Group, owned by Azerbaijan-born Russia magnate Aras Agalarov, who worked with the Trump Organisation in 2013 to host the Miss Universe pageant in Russia.
The encounter between Donald Trump Jr. and attorney Natalia Veselnitskaya was set up by Briton Rob Goldstone, a publicist associated with pop singer Emin Agalarov, the son of Aras.
Scott Balber, a US lawyer representing the Agalarovs, said Kaveladze attended the Trump Tower meeting at their request.
Balber said that he was contacted over the weekend by the office of Robert Mueller, the special counsel investigating alleged Russian interference in the 2016 election, with a request for the name of the Agalarov representative who was present for the meeting with Trump Jr.
Word of the enquiry from Mueller’s office is the first public signal that the special counsel is looking into the June 2016 discussion.
Trump Jr. was joined at the meeting by the president’s son-in-law Jared Kushner, and by Paul Manafort, who was then chairman of the Trump campaign.
Veselnitskaya asked Russian-American lobbyist Rinat Akhmetshin to accompany her and she also brought a translator, former US State Department employee Anatoli Samochornov.
Goldstone was also on hand.
Kushner, now a senior White House adviser, and Manafort are being targeted by investigators looking for evidence of alleged collusion between the Trump campaign and the Russian government.
In an interview last week with The Washington Post, Akhmetshin said that in the course of her work for clients, Veselnitskaya had discovered that a US hedge fund which “seemed linked to the (Democratic National Committee)” was operating in violation of Russian tax and securities law.
He added that Veselnitskaya “left a document behind” after the meeting with Trump Jr.
But Don Jr. said that Veselnitskaya turned out not to have any information on Clinton and was instead seeking to lobby the campaign on a separate matter.
Veselnitskaya said in an interview with NBC News that she had no links to the Kremlin and never possessed any incriminating information about the Democratic presidential candidate.
The main lobbying activity of both Veselnitskaya and Akhmetshin appears to be on behalf of Russian businesses who have been hurt by US sanctions.