Gov. Kelly Armstrong of North Dakota vetoed a bill this week that would have required most libraries in the state to keep material considered sexually explicit in areas difficult for minors to access. Under the measure, librarians who do not comply could have faced prosecution.

Mr. Armstrong, a Republican former congressman in his first year as governor, said in his veto message that the bill “represents a misguided attempt to legislate morality through overreach and censorship.”

“The bill imposes vague and punitive burdens on professionals,” Mr. Armstrong added in a letter dated Tuesday, “and opens the door to a host of unintended and damaging consequences for our communities.”

The legislature could override the veto with a two-thirds vote in both the Senate and House, but the bill passed the House with a narrow, 49-to-45 majority. Republicans hold large majorities in both chambers.

The legislation was part of a broader push by conservatives to restrict access to library books that they consider inappropriate for children, an effort that has alarmed many librarians and free speech advocates. New library laws or regulations have been approved in recent years in several Republican-led states, including Idaho, Iowa, South Carolina, Tennessee and Utah.