The House of Representatives passed the bill, which supports gender equality, on Mar 27.
The Senate voted 147-1 yesterday, with seven abstentions, to accept the bill. The debate was then adjourned for committee stages, reports the Bangkok Post.
The Senate is going into recess and the vetted legislation is expected to be returned for passage at the next session in July.
Senators agreed in principle to the bill, but some were concerned about issues such as necessary amendments to related laws once it becomes law.
Senator Piyachat Wanchaleom, a member of the committee on law, justice and police affairs, said more time may be needed for the law amendment period, which requires a thorough study by all affected state agencies.
Once it becomes law, Thailand will be the first country in Southeast Asia to allow same-sex marriage and only the third in Asia, after Taiwan and Nepal.
The bill could take effect within 120 days of royal endorsement.