"The reaction is a type of risk-off trade to buy the dollar and the yen against other currencies," said Masafumi Yamamoto, chief currency strategist at Mizuho Securities.
"Without additional stimulus, the U.S. economy will slow and the global economy will slow."
The dollar was last quoted at $1.1729 per euro, holding onto a 0.4% gain in the previous session.
The British pound was quoted at $1.2881 after skidding by 0.86% on Tuesday as optimism about Britain's trade negotiations with the European Union failed to shield sterling from the dollar's advance.
The dollar bought 0.9185 Swiss franc after rising 0.3% in the previous session.
Trump, still being treated for COVID-19, on Tuesday turned to Twitter to break off talks with Democrats on an aid package even though U.S. virus cases are rising.
Highlighting the peril, Federal Reserve Chair Jerome Powell on Tuesday warned that the U.S. economy could slip into a downward spiral if the coronavirus is not effectively controlled and called for more economic assistance.
Traders will look to minutes from the Fed's most recent meeting and comments from several Fed speakers later Wednesday for further signs of how central bankers view the outlook.
The increased risk aversion, however, did not move the dollar against the yen, which was last quoted at 105.67 JPY=D3 , because both currencies tend to be bought during times of uncertainty, analysts say.
Trading in other Asian currencies was mostly subdued, with financial markets in China closed for a public holiday.
Trump has only just returned to work on Monday after three nights in hospital following his bombshell admission last week that he had contracted the coronavirus.
Medical professionals have said Trump's early discharge from hospital puts others at risk of infection, and its spread among his most senior staff is swinging public opinion against him.
Support for his Democratic rival Joe Biden has grown by about four percentage points since mid-September, according to Reuters/Ipsos polling from Oct. 2 to 6, with 52% of likely voters backing Biden compared to 40% for Trump.
Investors are starting to warm up to the idea of Biden winning the election, which is a positive for the dollar, Mizuho's Yamamoto said.
The Australian dollar edged up to $0.7118 in Asian trade after tumbling by more than 1% on Tuesday. Traders say the Aussie faces more downside risks due to expectations that the Reserve Bank of Australia's next move is to cut rates and buy more government debt.
Across the Tasman Sea, the New Zealand dollar bought $0.6588, close to a one-week low.
(Reporting by Stanley White; Editing by Christopher Cushing and Sam Holmes) ((firstname.lastname@example.org; +81 (0)3 4563 2799; twitter.com/stanleywhite1 ;))