It was not immediately clear if Trump actually kept the award after the closed-door meeting.
The Norwegian Nobel Committee says its prizes cannot be transferred.
Acting Venezuelan President ‘not afraid’ of diplomatic clash
Trump had campaigned hard to win last year’s Nobel Peace Prize for what he says are his efforts to stop eight wars.
Instead it went to Machado, who appeared in Oslo last month to collect her prize – after a daring escape from Venezuela by boat – and then dedicated it to Trump.
Venezuela’s opposition has argued and presented evidence that Maduro stole the 2024 election from the candidate of Machado’s party, Edmundo Gonzalez Urrutia – claims supported by Washington.
But Trump has said Machado does not have enough support among Venezuelans, and he opted to stick with former Maduro loyalist Rodriguez.
Trump and Rodriguez had their first telephone call on Wednesday, and the White House said on Thursday that he “likes what he’s seeing” with Venezuela’s interim leaders.
However, Rodriguez said on Thursday that her Government was “not afraid” of a diplomatic clash with Washington.
“We know they are very powerful. We know they are a lethal nuclear power ... We are not afraid to confront them diplomatically, through political dialogue,” she said.
Rodriguez was delivering Maduro’s state of the nation address to Parliament while the toppled Venezuelan leader is in a New York jail facing drug trafficking charges.
By contrast, Machado, who campaigned for years to end leftist Maduro’s rule, was greeted by jubilant supporters as she left the White House.
And her meeting with Trump was an opportunity for her to bring the issue of a democratic transition back into the foreground.
White House press secretary Karoline Leavitt said as the lunch started that Machado was a “remarkable and brave voice for many of the people of Venezuela”.
But while Leavitt said Trump was “committed to hopefully seeing elections in Venezuela one day”, she would not give a timeline.
Sixth tanker seized
Since Maduro’s capture, Trump has said the US will “run” Venezuela – exerting pressure through a naval blockade and threats of further attacks – but has appeared content to let Rodriguez remain in power so long as oil keeps flowing.
US forces on Thursday seized a sixth oil tanker in their campaign to control the South American country’s critical fossil fuel sector.
Separately, the first US-brokered sale of Venezuelan oil, worth around US$500 million ($869.8m), has been finalised, a US official told AFP without identifying the buyer.
Rodriguez, in her speech, also announced plans for legal reforms to Venezuela’s oil sector – which currently limit the involvement of foreign entities – but did not give specific details.
Washington has also hailed the release of dozens of political prisoners in the past week, though hundreds remain behind bars.
Meanwhile, the shock waves from the lightning US raid that toppled Maduro continue to reverberate.
- Agence France-Presse