BUENOS AIRES—Argentina warned that relations with the U.S. could worsen because of ties that a White House appointee has to hedge funds that have been battling this country in U.S. courts.

In a letter written to U.S. President Barack Obama and made public late Friday, President Cristina Kirchner said that Nancy Soderberg had tried to undermine Argentina’s national interests as co-chairman of American Task Force Argentina, a lobbying group. ATFA, whose members include the hedge fund Elliott Management Corp.’s NML Capital Ltd.,...