Confirming the party's previous stance, the Social Democrats were the second party that, responding to an inquiry from the Justice Ministry, backed the idea of a gender-neutral Partnership Act.
The proposed legislation would not differentiate between heterosexual and homosexual couples.
The Reform Party's more conservative coalition partner, IRL, has expressed opposition to the idea, and the Centre Party, which has traditionally been a stronger supporter of gay rights, has not yet responded.
The Social Dems said they agreed with the position expressed earlier this year by the national ombudsman official, Chancellor of Justice Indrek Teder.
"Long-term cohabitation between people of the same sex is in an area protected by fundamental family law. As a result of this, a situation where such a cohabitation is not legally regulated is in conflict with the Constitution," reads the Social Democrats' response to Justice Minister Kristen Michal.
Michal had sent a letter to all four parties in Parliament in early August, proposing four alternatives to how to regulate marriage and cohabitation issues.
IRL's answer was brief, saying that it opposed any change to the current situation. The Reform Party said it backed the drafting of a gender-neutral Partnership Act, but wants to additionally discuss the issue of adoption.
The Reform Party also said it was open to the option of continuing with cohabitation and developing a number of standardized contracts people could use to handle the property-related issues that most frequently crop up.
The Social Democrats said this would not provide couples with sufficient protection under law.
Noting that Estonia already has de facto same-sex couples raising children, they noted that same-sex parents do not have an opportunity to adopt a partner's children. The death of one partner is a scenario, conjugal visits for detained persons and joint tax returns were issues that could not be addressed by a template contract, the Social Democrats said.