“If we can get regulatory clarity, I think it will sort of shepherd in or grandfather in some of these stablecoins that have been following best practices around being audited and regulated,” he said. 

So-called stablecoins are cryptocurrencies pegged to government-issued currencies on a one-to-one ratio. USD Coin is the world’s second-largest stablecoin with a $42.7 billion market capitalization. Tether is the largest stablecoin with a $65.7 billion market capitalization. 

On Thursday, the crypto exchange waived fees for retail customers to convert tether to USD Coin.

The battle for the stablecoin market has been heating up as interest rates continue to rise and the largest players jostle for market share. Since September, USD Coin has lost about $10 billion in market value, while tether’s market value remained flat, according to data provider CoinGecko. Overall this year, tether has lost about $13 billion in market value while USD Coin’s market cap was flat. 

Coinbase co-founded USD Coin with Circle Internet Financial in 2018. The exchange said in a Thursday blog that it is allowing customers to convert tether to USD Coin at no cost because it wants to make it easier for users to switch to a “trusted and reputable” stablecoin after the recent crash in the crypto markets eroded customer trust. 

A Tether spokesperson said: “This isn’t an honest competitive rivalry. This is a sad and desperate attempt from a company that is clearly suffering.”

Amid the collapse of rival exchange FTX, one unit of tether fell from $1 to as low as $0.9775 on Nov. 10 as traders rushed to withdraw tether. In May, during the $40 billion wipeout of TerraUSD and sister token luna, tether traded near $0.96 before later regaining its peg.

Mr. Armstrong said the firm’s move isn’t a comment on tether. “It’s just that we happen to have co-created USDC along with Circle and we have an economic interest in seeing that growth, and so we want to encourage people to use USDC,” he added. 

Tether has historically faced questions over the quality of the assets backing its dollar reserves. The stablecoin issuer also has been increasingly lending its own coins to customers rather than selling them for hard currency upfront, adding to the risks that it might not have enough liquid assets to pay redemptions in a crisis, The Wall Street Journal has reported. 

Write to Vicky Ge Huang at vicky.huang@wsj.com