Bills were introduced last week in the U.S. Senate and House would to repeal the 1996 Defense of Marriage Act parts of which the U.S. Supreme Court struck down in 2014. Titled “The Respect for Marriage Act,” the bills would repeal the remaining aspects of the law which directed the federal government to ignore same-sex marriages, and allows states without marriage equality to do the same.

The bill was introduced in the Senate by Sen. Dianne Feinstein, a Democrat from California. Both of Minnesota’s senators, Al Franken and Amy Klobuchar, have signed on to the bill and are listed as “original sponsors.” It has 44 co-sponsors total, all Democrats.

In the House, the bill was offered by Rep. Jerrold Nadler, a Democrat from New York. Minnesota Reps. Keith Ellison and Betty McCollum are listed among the 112 cosponsors as “original sponsors.” Only one Republican in the House, Rep. Ileana Ros-Lehtinen of Florida, has signed on in support.

If the bill becomes law, and DOMA is repealed, it would direct states without marriage equality to recognize same-sex marriages performed in other states.

“We must finish the job begun by the Supreme Court by passing the Respect for Marriage Act,” Rep. Nadler said in a statement last week. “The bill provides a uniform rule for recognizing couples under federal law, ensuring that lawfully married couples will be recognized under federal law no matter where they live and guaranteeing that all families can plan for a future of mutual obligation and support with confidence.”

“Only when this bill is passed will we be able to guarantee the federal rights, benefits and responsibilities of marriage for all loving couples,” Sen. Feinstein added. “I call on my colleagues on both sides of the aisle to support this bill.”