The Greek Justice Ministry pledged to establish a working group on the rights of gay couples living together, which would "analyze all aspects of the issue, international practice and the existing domestic legal and social framework."
The move follows a request by the country's National Commission for Human Rights that proposed a civil union registry that would allow both same-sex couples to marry. Parliament could approve the law in a few months, national media said
The current 1982 marriage law does not specify the gender of the groom and the bride. However, civil authorities refuse to marry same-sex couples. They say the move could result in a number of further legal difficulties, including the issue of adoption by gay couples.
The Greek Orthodox Church, which strongly opposes same-sex marriages, called the possibility a "catastrophic bomb" which threatened Greek society.
Modern Greece is a largely conservative society, strongly influenced by the dominant church. Civil marriages became legal just 15 years ago, while most Greeks still prefer a traditional Greek Orthodox wedding ceremony.
The first Gay Pride parade in Greece was held in 2005.