(CNN) -- The government of Argentina's capital will not appeal a court decision this week that legalizes same-sex marriage, Buenos Aires Mayor Mauricio Macri said Friday.

The court ruled that two articles in the city's civil code that say only people of different sexes can get married are illegal. The court decision applies only to Buenos Aires. Same-sex unions in most of the rest of Argentina remain illegal.

The legal challenge was initiated by a gay couple, Alejandro Freyre and Jose Maria Di Bello. Judge Gabriela Seijas ordered the city's civil registry department to honor their union.

"The law should treat each person with equal respect in relation to each person's singularities without the need to understand or regulate them," the judge said in her ruling.

The city code prevents people from "enjoying the rights that couples who enter into matrimony are entitled to," she said. Those rights include inheritances, pensions and the ability to make decisions for the other person when he or she is incapacitated.

Macri called the ruling a "very important step," adding that "we have to live together and accept reality. ... The world is headed in that direction."

His decision was not easy, Macri said. Many people wanted him to appeal.

"I had an important internal debate, weighing my upbringing with my search for the best customs and best liberties for society," he said in a videotaped message on his Facebook page.

"What we have to learn is to live in liberty without violating the rights of others," he said.

Macri likened the current debate over same-sex marriage to a similar discourse years ago.

"It's the same as happened with divorce several decades ago -- a very intense debate. And today it is something very natural," the mayor said.

Judge Seijas issued the ruling Wednesday but it did not become public knowledge until Thursday, when it was posted on the court's Web site.

Brazil, Colombia, Ecuador and Uruguay are also addressing the issue of same-sex civil unions.