WASHINGTON — The Supreme Court on Monday did not seem inclined to second-guess the denial of a visa on national security grounds to the Afghan husband of an American woman.

The State Department said in 2009 that it had turned down the husband, Kanishka Berashk, because he had been involved in terrorist activities, but it would not elaborate.

There was little question that Mr. Berashk was powerless to pursue the matter in American courts under a longstanding legal doctrine called “consular nonreviewability.” But his wife, Fauzia Din, a naturalized United States citizen, said the visa denial interfered with her fundamental right to marriage. A federal appeals court in California agreed, ruling that she was entitled to “a facially legitimate reason” for the denial.

At Monday’s argument, Justice Anthony M. Kennedy said he was uncomfortable with requiring the government to provide even minimal information, saying it “might give some indication as to our intelligence-gathering capability and the information that we have.”

Edwin S. Kneedler, a lawyer for the federal government, took a hard line on both of the basic questions in the case. Visa denials are never subject to court review, he said. He added that Ms. Din’s rights as a spouse are in any event too remote to allow her to sue.

Justice Sonia Sotomayor probed the first point, reminding Mr. Kneedler that the watch lists compiled since the Sept. 11 terrorist attacks include common names and errors.

“You’re telling us that there’s no remedy whatsoever for the alien to come in and try to show someone that he’s not the guy who’s the terrorist,” she said.

Mr. Kneedler responded that the State Department was careful and that the courts had no role to play.

Justice Stephen G. Breyer pursued the point. What if, he said, an American wife had “undeniable proof” that her husband’s visa had been denied “because the consular official believes that husbands and wives should live separately, or for racial reasons, or for First Amendment reasons?”

After Mr. Kneedler gave the same answer, Justice Antonin Scalia asked about what he called “an equally absurd hypothetical.” He listed the same reasons but added that “the man is not married and there is no wife who comes in and can make these points.”

That caused the argument to pivot to the second question, of whether Ms. Din can press claims her husband cannot.

Justice Breyer, responding to Justice Scalia, said the right to be married must count for something. “The result of this,” he said, “is that an American citizen either must live separately from her spouse forever or must give up her right as an American to live in her native land.”

But Mr. Kneedler said allowing the American spouses of foreigners to press their claims in court would be dangerous. “It would be a license for circumvention” of the usual approach, he said.

Several justices seemed inclined to agree, saying a wife cannot contest a husband’s criminal conviction because it would interfere with her marriage, even if both spouses are Americans.

Justice Ruth Bader Ginsburg added that prisoners had the right to marry but not the right to live with their spouses.

Chief Justice John G. Roberts Jr. asked Ms. Din’s lawyer, Mark E. Haddad, which other American family members could challenge visa denials of foreign relatives, suggesting that a decision for his client would result in many lawsuits. Mr. Haddad said parents, children who are minors and siblings might be entitled to file such suits.

In 1972, the Supreme Court did allow a group of American professors to contest the denial of a visa to a Marxist scholar they wanted to meet, citing the First Amendment. Justice Elena Kagan said the decision had not opened litigation floodgates and suggested that a ruling for Ms. Din in Monday’s case, Kerry v. Din, No.13-1402, might have a similarly modest effect.

But Justice Scalia said spouses were more tenacious than scholars. “Maybe there are more incentivized spouses than there are incentivized law professors,” he said. “Don’t you think that’s possible?”

Justice Kagan, a former dean of Harvard Law School, said she was not sure. “Law professors,” she said, “are very, very insistent.”