The couple thought it won the right to marry when a judge ruled that a ban on same-sex marriage violated Argentina’s Constitution.
The mayor of Buenos Aires, Mauricio Macri, said the city would not appeal, in effect inviting other same-sex couples to pursue their rights in court.
“We have to live with and accept this reality: the world is moving in this direction,” he said.
Mr. Freyre, 39, the executive director of the Buenos Aires AIDS Foundation, and Mr. Di Bello, 41, an executive with the Argentine Red Cross, sued after being denied a marriage license in April. Their request was granted by Judge Gabriela Seijas, who said that laws limiting marriage to a man and a woman violated the constitutional rights of equality.
The ruling sets no precedent beyond this case, but other gay and lesbian couples may cite it in court if their requests for marriage licenses are denied.
No other country in Latin America allows same-sex marriage, though some jurisdictions allow same-sex partners to form civil unions with many of the same rights.