Accompanying text read, "To President Donald J. Trump In Gratitude for Your Extraordinary Leadership in Promoting Peace through Strength," and labelled the gesture as a "Personal Symbol of Gratitude on behalf of the Venezuelan People".
A White House official confirmed that Mr Trump intended to keep the medal, Reuters reported.
The pair met at the White House on Thursday, local time, for lunch before Ms Machado left to meet senators at the Capitol.
As she left that second meeting and was swarmed by media, she said she had presented Mr Trump with the esteemed prize in "recognition [of] his unique commitment [to] our freedom".
Ms Machado then referenced the 200-year-old gifting of a different medal by the
Marquis de Lafayette, a general who fought against the British in America's Revolutionary War, to South American revolutionary leader Simón Bolívar, to signify the pair's shared values.
Venezuela's new leader says political prisoners are being freed, but hundreds remain jailed, with families clinging to hope that pressure from the US will eventually secure their loved ones' release
"It was given by General Lafayette as a sign of the brotherhood between the people of the United States and the people of Venezuela in their fight for freedom against tyranny," she said.
In an interview with Fox News afterwards, Ms Machado said "he deserves it, and it was a very emotional moment".
Ms Machado was awarded the 2025 Nobel Peace Prize in October for her "tireless work promoting democratic rights for the people of Venezuela and for her struggle to achieve a just and peaceful transition from dictatorship to democracy".
She fled Venezuela late last year and has been pressing the US to help advance a democratic transition after the capture of long-time Venezuelan President Nicolás Maduro.
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