The new legislation, written by Sen. Dianne Feinstein (D-Calif.), is called the Respect for Marriage Act.
Currently, same-sex couples can't file joint federal tax returns or be protected under the Family and Medical Leave Act, which guarantees workers' right to take unpaid leave for family and medical reasons without fear of losing their jobs.
But the legislation, which might continue to advance in the Democratic-controlled Senate, is likely to die in the Republican-controlled House.
Sen. Orrin G. Hatch (R-Utah) was one of eight members of the committee to oppose the legislation Thursday.
"Under this bill, for the first time, millions of Americans living in states that have chosen to affirm traditional marriage would be forced to subsidize federal rights and benefits for individuals in same-sex marriages," Hatch said. "That's why I opposed this bill today and will continue to support DOMA."