Bitcoin, which had fallen as much as 2.9 per cent before Mr Musk’s tweet, briefly erased losses before retreating again.
Ether was up as much as 2.3 per cent before giving up some gains.
Dogecoin’s 3.8 per cent increase over the past hour was the biggest among cryptocurrencies tracked by CoinGecko.
Last May, he said he hasn’t “and won’t” sell any Dogecoin, a token created in 2013 as a joke and for which he’d become a proponent.
In October, Mr Musk said he owns Bitcoin, Ether and Dogecoin.
This time around, he had posted a question on Twitter about the likely rate of inflation over the next few years.
Michael Saylor, chief executive of MicroStrategy and a prominent Bitcoin bull, replied: “Weaker currencies will collapse and the flight of capital from cash, debt and value stocks to scarce property like #bitcoin will intensify.”
“It is not entirely unpredictable that you would reach that conclusion,” Mr Musk retorted.
MicroStrategy took a $147 million impairment charge for the fourth quarter as Bitcoin’s price drop forced the company to write down its holding in the cryptocurrency.