"And there, the viral infection rate is still up in the air, (and) it's a bit of risk-aversion."
The safe-haven Japanese yen rose 0.5% to 107.41 yen per dollar. Both the dollar and yen gained strongly against emerging market currencies.
The weekend brought more bad news on the virus front. Total deaths are nearly 34,000. The United States has emerged as the latest epicentre, with more than 137,000 cases and 2,400 deaths and lockdowns are toughening worldwide.
Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases, said the pandemic could ultimately kill between 100,000 and 200,000 people in the United States, if mitigation was not successful.
U.S. President Donald Trump, who had talked about reopening the economy for Easter, on Sunday extended guidelines for social restrictions to April 30.
The yen rose nearly 1% against the Australian dollar and nearly 2% against the Korean won with the mood.
"Risk aversion is likely to stay elevated with the U.S. the epicentre of COVID-19," National Australia Bank analysts said in a note.
The Chinese yuan also slipped 0.3% in offshore trade to 7.1080 after the People's Bank of China unexpectedly cut a key interbank interest rate, the seven-day reverse repurchase rate, by 20 basis points.
The Singapore dollar jumped briefly after the city-state's central bank eased policy, as expected, but emphasised stability rather than foreshadowing further easing.
KING DOLLAR DETHRONED
The dollar's modest gains on Monday barely recover a fraction of the ground it gave up last week, yet that slump followed a massive surge that leaves the U.S. currency still elevated.
Over the past two weeks the dollar first posted its biggest weekly rise since the 2008 financial crisis and then its biggest weekly drop since 2009. Signs of funding stress have eased but not abated as hard cash remains in high demand.
"Risk aversion has been more important to the direction of the dollar than traditional interest rate differentials," Standard Chartered analysts said in note.
"For the dollar to surrender some of its recent gains, investors would need to shift their preferences back to a broader basket of safe-haven assets."
Monday's moves showed some hint of that, since dollar gains came in tandem with a rising yen and rallying bonds.
Yields at the very short end of the U.S. curve dipped into negative territory and the benchmark 10-year yield fell nearly 9 basis points to 0.6605%. Gold was flat.
Against a basket of currencies the dollar rose 0.3% to 98.641.
(Reporting by Tom Westbrook Editing by Shri Navaratnam and Sam Holmes) ((firstname.lastname@example.org; +65 6318 4876;))