(CNN) -- The Illinois Senate passed a measure Thursday to legalize same-sex marriage, voting 34-21.
The state House will consider it next. Gov. Pat Quinn, a Democrat, has indicated he would sign the bill.
Illinois would be the 10th state, plus the District of Columbia, to legalize same-sex marriage, according to Lambda Legal, a gay rights organization.
Three other states are considering similar legalization, said Camilla Taylor, marriage project director for Lambda Legal. A bill has passed the Rhode Island House and been sent to the Senate. A proposal has been introduced in the Hawaii legislature, and another is expected in Delaware, Taylor said.
Five states, including Illinois, have civil union laws, according to Lambda Legal and the National Conference of State Legislatures. The others are Hawaii, Delaware, New Jersey and Rhode Island.
The groups list four states as having some type of domestic-partnership recognition: California, Oregon, Nevada and Wisconsin. Lambda Legal lists Colorado as recognizing designated beneficiary agreements.
Twenty-nine states have constitutional provisions banning same-sex marriage, the National Conference of State Legislatures says.
Polls show that legalizing same-sex marriage is gaining support across the country.