Congressional backers of a proposed Smithsonian-affiliated museum devoted to the history and culture of American Latinos didn't succeed the first time around, so they're trying again.

The bipartisan bills resubmitted Friday in the U.S. House and Senate aim to designate an unused, 132-year-old Smithsonian building on the National Mall in Washington as the future site of an American Latino Museum.

If passed, it would not commit the federal government to build and fund the museum. Instead, it would designate the historic Arts and Industries building as its main site, and launch a planning process by the Smithsonian’s Board of Regents to consider design and construction issues and funding....