Bitcoin hit a high of $US105,142 ($A165,390) and last traded at $US104,609.
The price rose on news reports over the weekend that Trump would go ahead with a bitcoin strategic reserve fund, according to Tony Sycamore, an analyst at IG.
"We're in blue sky territory here," Sycamore said on Monday.
"The next figure the market will be looking for is $110,000. The pullback that a lot of people were waiting for just didn't happen, because now we've got this news."
Bitcoin has surged more than 50 per cent since the November 5 election that saw Trump elected along with many other pro-crypto candidates.
"We're gonna do something great with crypto because we don't want China or anybody else - not just China but others are embracing it - and we want to be the head," Trump told CNBC late last week.
When asked if he plans to build a crypto reserve similar to oil reserves, Trump said: "Yeah, I think so."
The cryptocurrency industry spent more than $US119 million backing pro-crypto US congressional candidates, hoping to boost those who would pass crypto-friendly bills to promote digital assets.
Trump this month named a White House czar for artificial intelligence and cryptocurrencies, former PayPal executive David Sacks, a close friend of Trump adviser and megadonor Elon Musk.
