Wednesday night, the house voted 85-63 to pass the bill, which extends the equivalent of marriage rights to gay and lesbian couples, the Hartford Courant reported.
The senate, which passed the measure 27-9 last week, is expected to approve it again as amended, and the new amendment was also welcomed by Gov. Jodi Rell, the newspaper said.
Rell pledged to sign the bill into law if the senate accepts the house version.
On the amendment to define marriage as a union of a man and a woman, the House voted 80-67. Within parties, Republicans voted in favor 47-4, with one absence, and Democrats voted against it 63-33, with three absences.
Brian Brown, executive director of the Family Institute of Connecticut, which opposes civil unions and gay marriage, said adding the marriage definition was paying lip-service to opponents.
"It's still same-sex marriage in everything but name," Brown said.