Justice Sonia Sotomayor asked about the failure to disclose an embarrassing childhood nickname. Justice Elena Kagan said she was a “little bit horrified to know that every time I lie about my weight it has those kinds of consequences.”

Mr. Parker said the law applied to all false statements, even trivial ones.

Justice Stephen G. Breyer said it was “rather surprising that the government of the United States thinks” that the naturalization laws should be “interpreted in a way that would throw into doubt the citizenship of vast percentages of all naturalized citizens.”

Chief Justice Roberts added that the government’s position would give prosecutors extraordinary power. “If you take the position that not answering about the speeding ticket or the nickname is enough to subject that person to denaturalization,” he said, “the government will have the opportunity to denaturalize anyone they want.”

The Trump administration has sought to strip the citizenship of a convicted terrorist, and President Trump has said that loss of citizenship may be a fit punishment for burning the American flag.

Wednesday’s case concerned Divna Maslenjak, an ethnic Serb who said she had faced persecution in Bosnia. She was granted refugee status at least partly on that basis in 1999 and became a United States citizen in 2007.

Along the way, she apparently lied about her husband, saying she and her family had also feared retributions because he had avoided conscription by the Bosnian Serb military. In fact, he had served in a Bosnian Serb military unit, one that had been implicated in war crimes.

When this came to light, Ms. Maslenjak was charged with obtaining her citizenship illegally. She sought to argue that her lie was immaterial, but the trial judge told the jury that any lie, significant or not, was enough. Ms. Maslenjak was convicted, her citizenship was ordered revoked, and she and her husband were deported to Serbia.