Connecticut lawmakers who passed strict new gun control measures in response to the Sandy Hook Elementary School massacre approved a package of revisions Monday to reduce confusion about the new rules and expand the list of officials who can legally possess restricted firearms.

Both chambers of the state legislature voted to adopt changes and exemptions to the bipartisan deal that strengthened the state’s assault weapons ban and banned the sale of high-capacity magazines.

The legislation emerged from a bipartisan working group that sought to refine the original gun control bill, which proponents hailed as one of the most far-reaching in the nation, in response to ambiguity that came to light in part through feedback from constituents and gun owners. A spokesman for Gov. Dannel P. Malloy said he supports the changes.