The Trump and Melania cryptocurrencies, the latter which was launched on Sunday, were created on the Solana blockchain.
The price of Solana's coin also rose over the weekend, hitting an all-time high of $294.33 on Sunday.
"I think in the short term there's a chance this could be a sell-the-news event," said Matthew Dibb, chief investment officer at crypto asset manager Astronaut Capital, adding that crypto investors had been anticipating some executive actions to be rolled out during Trump's first day in office.