Washington — The Supreme Court agreed Monday to consider reviving part of a new federal law that makes it a crime to send computer messages that offer child pornography, even when no pornography exists.

Last year, a federal appeals court in Atlanta struck down this provision on free-speech grounds and said it reached too far. The judges said the law could be read to make it illegal for a grandfather to send a message that said, “Good pics of kids in bed,” when he was referring to innocent photos of his grandchildren in their pajamas.

But Justice Department lawyers said that example itself is far-fetched and should not stand in the way of a needed measure to combat the trafficking in child pornography.

The court voted to hear the government’s appeal, although arguments in the case will not be heard until the fall.

This is only the latest in a series of legal disputes over how to combat child pornography without infringing on the freedom of speech protected by the First Amendment.

Five years ago, the court struck down part of the anti-pornography law that extended to computer-generated images. Since no children were involved in creating these images, they could not be prohibited by law, the justices said.

The next year, Congress passed a revised law. One provision was targeted at computer users who offer or solicit child pornography. It says, “Any person who knowingly advertises, promotes, presents, distributes or solicits … a visual depiction” of a child engaged in sex commits a crime, whether or not the material exists.

Justice Department lawyers said this provision has been used “only rarely to date,” but they also said it gives prosecutors an extra weapon for charging would-be traffickers even when the obscene images cannot be located.

John Mitchell, a south Florida man, pleaded guilty to two violations of the child pornography law, one for “advertising” on the computer nude photos of his 4-year-old daughter and the other for possessing child pornography on a computer disk. He was sentenced to five years in prison.

His lawyer appealed and argued that the “advertising” part of the law was too broad. A three-judge panel in Atlanta agreed on the grounds that, in theory, it could punish persons who merely discuss or send messages about pornography that does not exist.

Those who traffic in “what purports to be child pornography deserve no sanctuary,” said U.S. Solicitor General Paul Clement, who urged the court to uphold the full law as constitutional.