Without Clara Tauson, who is rehabilitating from an injury, a young Danish national team lost 1-2 to Mexico in the first match of a three-nation tournament that also features Canada.
The winner of the mini-tournament in Monterrey, Mexico, secures entry into a qualifying tournament for the final event, the Billie Jean King Cup Finals.
Denmark otherwise got off to a promising start against the Mexican hosts when Rebecca Munk Mortensen beat Victoria Rodriguez 6-4, 6-4.
The 20-year-old Dane, ranked 652nd in the world, showed composure as both the first and the second set went to the wire.
Munk Mortensen only needed a single set point to decide the first set, and the same came true in the second set.
Johanne Svendsen, a year older than Mortensen, then faced Mexico's strongest card, Renata Zarazua, who is ranked 70th in the world.
The underdog Dane, who is ranked 554th in the world, got off to a terrific start and won the first set. But it ended in a Danish defeat 7-5, 3-6, 3-6 against the experienced Zarazua.
The match was then to be decided in a doubles match where Rebecca Munk Mortensen and Johanne Svendsen were defeated by Zarazua and doubles specialist Giuliana Olmos. The Mexicans won 6-3, 7-5.
Before leaving for Mexico, the sports director of the Danish Tennis Association, Jens Anker Andersen, had lowered expectations for the Danish national team after Clara Tauson announced her withdrawal last week.
Denmark's next match against Canada at the mini-tournament in Monterrey begins on Saturday at 23:00 CET