"At the moment, hopes for economic recovery are strong, but I expect this to gradually fade to increased concern about the U.S.-China relationship," said Minori Uchida, head of global market research at MUFG Bank in Tokyo.
"When that happens, there will be more risk-off trades, which supports buying of both the dollar and the yen."
The dollar stood at $1.1083 per euro in Asia on Friday, close to its lowest since March 30.
The common currency was headed for its second weekly gain against the greenback as the EU's announcement of a 750-billion-euro coronavirus recovery fund fuelled optimism about the euro-zone economy.
The dollar last bought 0.9632 Swiss francs, on course for a 0.8% weekly decline.
The greenback was little changed at 107.43 yen.
The Australian dollar bought $0.6630, close to its highest in more than two months, while the New Zealand dollar traded at $0.6204, near its strongest since March 11.
The Aussie and the kiwi were on course for weekly gains as investors cheered the gradual re-opening of business activity in the two antipodean economies.
Japan's currency crept higher against the euro, the Aussie and the kiwi, supported by safe-haven flows in relatively subdued trade.
China's parliament on Thursday approved national security legislation for Hong Kong that Western countries fear could erode the city's freedoms.
Trump, who has vowed a tough U.S. response, told reporters he would hold a news conference on China on Friday.
The risk is Hong Kong could lose some of the special privileges in enjoys under U.S. law, which would threaten its status as a global financial hub.
The potential stand-off has stirred memories of last year's bruising Sino-U.S. trade war, which weighed on the global economy and roiled financial markets.
In the onshore market, the yuan edged lower to 7.1515 against the dollar. Offshore, the yuan traded at 7.1674, not far from a record low of 7.1966 reached on Thursday.
This week the euro led the charge against a weakened dollar after EU policymakers unveiled fiscal stimulus combining grants and loans intended to ease dissent among euro-zone countries.
Analysts say the euro may struggle to extend its gains, because fiscally conservative member states may still push to alter the plan.
Some traders will focus on the release of German retail sales and EU consumer prices later on Friday to measure the health of the euro-zone economy.
Elsewhere, the pound held steady at $1.2327. Sterling was on course for its second weekly gain, supported by broad selling in the dollar this week.
However, sentiment for the pound has been somewhat negative due to calls for the resignation of an influential aide to British Prime Minister Boris Johnson, lack of progress in EU trade talks, and speculation about negative interest rates.
(Reporting by Stanley White; editing by Richard Pullin) ((firstname.lastname@example.org; +81 (0)3 4563 2799; twitter.com/stanleywhite1 ;))