The price of the digital currency bitcoin crossed over the $4,000 mark for the first time in its nine-year history, despite a widespread selloff in other major digital currencies.

Bitcoin was trading Sunday morning near $4,033, according to the news and research site CoinDesk, up 3.1% on the day, and up more than 25% in August. The price, which rose as high as $4,200 Sunday morning, has more than quadrupled so far this year.

Unlike...