USD edged up against most of its major rivals in the European session on Monday as worries about a spike of Delta variant infections in Asia kept investors' risk appetite in check.

The U.S. Dollar Index (DXY), measuring the U.S. currency's value relative to a basket of foreign currencies, edged up 0.07% to 91.91.

Australia's largest city, Sydney, started a fresh two-week lockdown on Saturday due to concerns over the Delta variant virus cases, while Thailand imposed new restrictions for a month to prevent the new virus outbreak. In addition, reports say that Tokyo may soon see a new state of emergency declared and that Hong Kong is to ban all travelers from Britain from July 1 to keep out Covid-19 variants.

In Europe, Germany's Chancellor Angela Merkel reportedly aims to advance a plan that restricts British travelers from the EU.

Market participants also remain cautious, awaiting the release of the key U.S. payrolls data, which is due later this week. Economists are forecasting that nonfarm payrolls increased by 683,000 in June.