The Respect for Marriage Act was introduced in the Senate and the House of Representatives, Human Rights Campaign said. The Obama administration has already announced it will enforce the Defense of Marriage Act but not defend it from legal challenges.
A poll conducted for Human Rights Campaign found just over half of the U.S. public, 51 percent, opposes DOMA and 34 percent support it.
DOMA, which defines marriage as the union of a man and a woman and says states do not have to recognize gay marriages from other jurisdictions, became law in 1996. Eight years later, Massachusetts became the first state where same-sex marriages are legal, and four states and the District of Columbia have followed suit.
"The debate over DOMA isn't about whether you favor marriage equality, it's about whether the government can pick and choose which marriages they like, and which they don't," said rights campaign President Joe Solmonese.
Because of DOMA, same-sex couples cannot take advantage of more than 1,000 federal rights and benefits available to married couples. They include sponsoring a gay partner for immigration and filing joint income tax returns.
Congressional Republicans have said they will hire lawyers to defend DOMA.
2014: The Year in Music [PHOTOS]