WASHINGTON — The Supreme Court Tuesday will take up a First Amendment test of Congress’ ability to tackle child pornography in the digital age.

Justice Department lawyers defending a 2003 law that criminalizes the advertising of purported child porn say such Internet ads fuel the market for smut and hurt children even when the advertised pictures are fake.

Challengers to the law, including the National Coalition Against Censorship and the American Booksellers Foundation for Free Expression, counter that it sweeps too broadly. They say it threatens the marketing of Lolita and other fictional depictions of adolescent sex.

At stake is Congress’ latest attempt to prohibit sexual content on the Internet. Backed by 28 states, U.S. Solicitor General Paul Clement stresses the need to curtail the marketing of child porn to protect the children abused to create it.

Clement, who will argue the case today, stressed in a written filing that because of the Internet “the distribution of child pornography has expanded exponentially.” He said even fraudulent offers to buy or sell child porn feed the market.

On the other side, backing a Florida man convicted for promoting pornography, are free-speech advocates who say the law could be used against marketers of mainstream literature or movies.

“Consider … the promotional speech on the DVD cover of the film Cruel Intentions that talks of the ‘ultimate challenge to … deflower the headmaster’s beautiful, virgin daughter,’ played by Academy Award winner Reese Witherspoon,” wrote New York lawyer Michael Bamberger, on behalf of the American Booksellers Foundation and other publishing groups.

For the past decade, Congress has aggressively targeted sexual materials on the Internet to shield children. Legislation has divided into two general categories: laws intended to stem the tide of illegal child pornography, as in the current case, and laws aimed at keeping pornography containing adult images away from children who roam the Web. Unlike pictures of minors, pornographic images of adults are legal.

In crafting these laws, Congress has confronted First Amendment hurdles. Since 1997, the Supreme Court has invalidated various provisions as too broadly written, potentially chilling speech or impinging on adult rights to pornographic pictures of adult men and women.

In 2002, for example, the court rejected a 1996 law against “virtual” child porn because Congress so loosely defined the materials that the court found the prohibition might have covered depictions of Shakespeare’s Romeo and Juliet.

The current challenge arises from Congress’ attempt to rewrite the 2002 statute. Part of the disputed provision makes it a crime — punishable by at least five years in prison — to advertise, promote, distribute or solicit materials purported to show children in sexually explicit acts.

The government says the ban is especially important in the digital age. Child pornography, which was nearly stamped out by the mid-1980s, has rebounded online, the Justice Department reports.

The law was challenged by Michael Williams, who was caught in 2004 in a federal sting after first putting out this message in a chat room: “Dad of toddler has ‘good’ pics of her and me for swap of your toddler pics, or live cam.” After other incriminating messages, agents obtained a search warrant for Williams’ home and found several images of children under age 18 engaged in sexual activity.

Williams was arrested and convicted of possession of child pornography, as well as the illegal promotion of it. He received two five-year prison terms.

Williams claimed the provision barring the promotion of child pornography was unconstitutional because it could cover non-existent or clean pictures. The U.S. Court of Appeals for the 11th Circuit agreed. In a decision last year, it said the law violated the First Amendment free-speech guarantee.

The appeals court emphasized the law could reach fake porn offerings and also non-commercial e-mails, such as “Good pics of kids in bed” sent by a grandparent and attached to innocent pictures of children in pajamas.

Clement insists the hapless grandparent would not be in trouble because the law targets only people who believe they have real child porn or who want potential buyers to believe it’s the real thing.

He dismissed the concerns of outside groups about movie advertising by noting that producers of mainstream movies do not intend for viewers to believe that real children are actually engaging in sex in their movies.

Richard Diaz, Williams’ lawyer, contends the statute “criminalizes a person’s desire to brag or lie” about materials offered.

Eugene Volokh, a law professor at the University of California, Los Angeles, who specializes in First Amendment issues, says the outcome is likely to depend on whether the court accepts the Justice Department’s view that the law’s reach is narrow.

“If the law is limited to people who believe that something is child porn or who want others to believe it is child porn, it would be constitutional as effectively a ban on the soliciting of a crime,” he says. “If the law is read as broader, it likely would be unconstitutional.”