Though there have been many warnings about a bitcoin "bubble", including from European Central Bank Deputy Governor Vitor Constancio, some say it has much further to climb. But determining its value is difficult.
"For most currencies there are several accepted methodologies for estimating relative value, normally based on macroeconomic fundamentals," said EFG Asset Management's Global Head of Research, Daniel Murray. "For bitcoin no such fundamentals exist."
Other cryptocurrencies -- whose prices tend to be highly correlated to bitcoin -- also rallied. Their total value -- or market capitalization -- climbed above US$160 billion for the first time since early September, according to industry website Coinmarketcap.com.
Two upcoming "forks" in the bitcoin software code, which will create rival clones of the cryptocurrency, were seen by some as a reason for the rise in price, which saw a boost after the "Bitcoin Cash" clone was created at the start of August.
"Investors are seeing the lessons of history in the up-and-coming forks and hoping for an extra dividend," said Charles Hayter, co-founder of data analysis website Cryptocompare, adding that rumors on online forums that China could reopen exchanges could also be affecting the price.
(By Jemima Kelly; Additional reporting by Jamie McGeever; Editing by Catherine Evans)