The Senate is likely to approve a 10-year extension of the ban, which expires Monday, when it returns to Washington next week, the Washington Post reported Tuesday.
It's the first piece of firearms legislation both houses have agreed on following the mass shootings at Sandy Hook Elementary School in Connecticut last December, but at least one lawmaker said the bill didn't go far enough.
In a statement before the House voted, Sen. Charles Schumer, D-N.Y., said, "The House bill is better than nothing, but it's not good enough."
Schumer said the legislation should have included weapons made with 3-D printers.
He said he plans to introduce a bill to deal with new technologies such as 3-D printing that are capable of reproducing metal weapons in plastic, the Post said. While such firearms could not be detected by security devices such as those found at airports, they would be capable of firing real shells.