Bitcoin has risen 13 per cent, recovering about half of the losses it sustained last week, its worst since 2013, as investors who missed out on earlier rallies bought the world's biggest and best-known digital currency.

While bitcoin investors and analysts believe last week's decline in its value was a natural correction after a heady run-up in prices, there have been further warnings from market regulators and central banks.

Bitcoin fell nearly 30 per cent at one stage on Friday to $US11,159.93 ($A15,623.90). On Tuesday, bitcoin was up 13 per cent at $US15,630.00 in light trading on the Luxembourg-based Bitstamp exchange.

The digital currency had risen around twentyfold since the start of the year, climbing from less than $US1,000 to as high as $US19,666 on Dec. 17 on Bitstamp and to over $US20,000 on other exchanges.

Meanwhile, critics have pointed to bitcoin's design flaws and hacks of digital "wallets" in which bitcoins are kept as an alternative to traditional currencies.

Shmuel Hauser, the chairman of the Israel Securities Authority, was the latest among regulators to voice his concerns. He said on Monday he will propose regulation to ban companies based on bitcoin and other digital currencies from trading on the Tel Aviv Stock Exchange.

Singapore's central bank last week issued a warning against investment in cryptocurrencies, saying it considers the recent surge in prices to be driven by speculation and that the risk of a sharp fall in prices is high.

Prices of other cryptocurrencies, which slid along with bitcoin last week, have also recovered, with Ethereum, the second-biggest cryptocurrency by market size, quoted around $US771, up from Sunday's low of $US689 but still far from highs around $US900 hit last week.