LONDON—The U.S. dollar recouped some overnight losses and the euro gained for a second day on Tuesday as risk sentiment recovered partially after a selloff in global markets. Major currencies held within well-worn trading ranges, however, as a surge in cases of the Omicron coronavirus variant forced countries to reimpose restrictions, raising concerns over the near-term economic outlook. Risk appetite took a blow on Monday after U.S. Senator Joe Manchin, a moderate Democrat who is key to President Joe Biden’s hopes of passing a $1.75 trillion domestic investment bill—known as Build Back Better—said on Sunday he would not support the package prompting a selloff in global markets. “Tuesday’s reversal comes after U.S. Senator Manchin puts forward proposals to support President Biden’s $1.75 trillion fiscal bill with poor liquidity probably exaggerating some of yesterday’s moves,” said Kenneth Broux, an FX strategist at Societe Generale. The dollar index, which measures the currency …