More than 4,000 people rallied Thursday in Cordoba to urge the Argentine Senate to approve a gay marriage bill, various media outlets reported.

Demonstrators marched on the Plaza de la Intendencia, where they held banners, chanted slogans and listened to speeches in favor of making Argentina the first Latin American country to legalize marriage between two members of the same sex.

The bill was approved in May by Argentina's lower house, the Chamber of Deputies (la Camara de Diputados). The Senate General Law Committee reviewing the bill has taken its gay marriage debate on the road, with stops planned for the cities of Salta, Tucuman, San Juan and Mendoza. The four-city tour runs from June 14-28. The full Senate is scheduled to take up the bill on July 14, a Wednesday, where the measure faces an uncertain future.

Argentine President Christina Fernandez de Kirchner has said she would not block the measure from becoming law, if approved by senators.

Lawmakers in favor of gay marriage also spoke at the rally.

“Today nobody can say the existence of same-sex couples is abnormal,” Cordoba National Deputy Paula Cecilia Merchan told the crowd. “We are fighting, and I think we will ensure that the law is approved, so that these couples are recognized in the same way heterosexual couples are. In that sense, I think this fight has more to do with reality and cultural and social conditions.”

Uruguay recognizes gay couples with civil unions and lawmakers legalized gay marriage in Mexico City last December. Chile is considering a civil unions law.