The meeting followed the two leaders’ formal two-hour meeting on 7 July in which Mr Trump said Mr Putin denied allegations that he directed efforts to meddle in the 2016 US presidential election.
The second meeting, which took place some hours later, was only attended by Mr Putin, Mr Trump and Mr Putin’s translator. It had not previously been disclosed by the White House.
The White House official did not say how long the second meeting took place or what was discussed.
The second meeting between Mr Putin and Mr Trump was first reported by Ian Bremmer, president of the Eurasia Group.
Mr Bremmer said the meeting, which went ahead without Mr Trump’s own translator present, was a breach of national security protocol, though he added that it was one the president likely would not know about.
Their formal meeting - their first face-to-face talks amid investigations in the US into possible collusion between Russia and Trump campaign figures during last year's presidential vote - lasted more than two hours, despite being scheduled for only half-an-hour.
At one point, First Lady Melania Trump entered the room to hurry them along.
Afterwards, Russia's foreign minister Sergey Lavrov claimed Mr Trump accepted Mr Putin’s assurances that Russia did not meddle in the US presidential election - a claim later denied by the White House.
However, US Secretary of State Rex Tillerson said Mr Trump had raised the issue of Moscow’s alleged cyber-meddling in the election at the start of their conversation.
He said the US had talked about such attacks represented a “threat to the democratic process”.
“I think the president is rightly focused on how do we move forward from something that may be an intractable disagreement at this point,” Mr Tillerson said.
The President later hit out at negative coverage of the previously undisclosed discussion, writing on Twitter: "Fake News story of secret dinner with Putin is 'sick.' All G 20 leaders, and spouses, were invited by the Chancellor of Germany. Press knew!"
A few minutes later he added: "The Fake News is becoming more and more dishonest! Even a dinner arranged for top 20 leaders in Germany is made to look sinister!"
National Security Council spokesman Michael Anton said: "A conversation over dessert should not be characterised as a meeting."
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies