It was not immediately clear whether Trump had accepted the medal. Machado, who described Thursday's meeting as "excellent," told reporters she had done so in recognition of his commitment to the freedom of the Venezuelan people.
Her gesture appeared to be part of her effort to gain influence over the future direction of her country. Trump openly campaigned for the prize before Machado was awarded it in December.
Even if Machado gave Trump her medal, the honour remains hers. The Norwegian Nobel Institute has said the prize cannot be transferred, shared or revoked. Asked on Wednesday if he wanted Machado to give him the prize, Trump told Reuters: "No, I didn't say that. She won the Nobel Peace Prize."
The lunch meeting, which appeared to last slightly over an hour, marked the first time the two have met in person. Machado then met with more than a dozen senators, both Republican and Democratic, on Capitol Hill, where she has generally found more enthusiastic allies.
While the visit was ongoing, White House press secretary Karoline Leavitt said Trump had been looking forward to meeting Machado, but that he stood by his "realistic" assessment that she did not currently have the support needed to lead the country in the short term.
Machado, who fled Venezuela in a daring seaborne escape in December, is competing for Trump's ear with members of Venezuela's government and seeking to ensure she has a role in governing the nation going forward.
After the US captured Venezuela's longtime leader, Nicolas Maduro, in a snatch-and-grab operation on January 3, various opposition figures, members of Venezuela's diaspora and politicians throughout the United States and Latin America have expressed hope that Venezuela will begin the process of democratisation.
"I know the president was looking forward to this meeting, and he was expecting it to be a good and positive discussion with Miss Machado, who is really a remarkable and brave voice for many of the people of Venezuela," Leavitt told reporters during a briefing as the meeting was ongoing.
Democratic Senator Chris Murphy, one of the senators who met with Machado, said the opposition leader had told senators that repression in Venezuela was no different now than under Maduro.
Venezuela's interim President Delcy Rodriguez is a "smooth operator" who was growing more entrenched by the day thanks to Trump's support, he said.
"I hope elections happen, but I'm sceptical," said Murphy, of Connecticut.
Trump has said he is focused on securing US access to the country's oil and economically rebuilding Venezuela. Trump has on several occasions praised Rodriguez, Maduro's second-in-command, who became Venezuela's leader upon his capture.
In an interview with Reuters on Wednesday, Trump said, "She's been very good to deal with."
Separately in Venezuela, Rodriguez said she would propose reforms to her country's oil industry.
Machado was banned from running in Venezuela's 2024 presidential election by a top court stacked with Maduro allies. Outside observers widely believe Edmundo Gonzalez, an opposition figure backed by Machado, won by a substantial margin, but Maduro claimed victory and retained power.
While the current government has freed dozens of political prisoners in recent days, outside groups and advocates have said the scale of the releases has been exaggerated by Caracas.
