The deep throat saliva samples would be collected when crews arrive in Hong Kong, the city's health officials said Tuesday. If crew members test positive they would be hospitalized there.
The requirements are the latest obstacle to resuming regular international flights since the coronavirus pandemic upended air travel earlier this year.
United said it suspended its service to and from Hong Kong through July 10.
"We are currently assessing how this impacts our future operations," the airline said Thursday in a statement.
American pushed back service between Dallas/Fort Worth and Hong Kong from Thursday to Aug. 5. It had suspended service to Hong Kong in February.
"We've been making regular adjustments to our schedule to match demand, and we consider a range of factors including travel restrictions or entry requirements in making network decisions," American said in a statement Thursday.
American Airlines pilots' labor union, the Allied Pilots Association, said it discussed concerns about the testing requirements with management.