Law enforcement officials grew concerned this week that the Wisconsin school shooting on Monday may have been part of a broader plot that could have included an attack on a government building, according to a court document filed in California.

As F.B.I. agents pursued leads after the shooting at Abundant Life Christian School in Madison, they found messages that the shooter, Natalie Rupnow, 15, exchanged online with a 20-year-old man in the San Diego area, according to the document.

Agents detained and questioned the man on Tuesday. The man told investigators that “he told Rupnow that he would arm himself with explosives and a gun and that he would target a government building,” an officer from the Carlsbad Police Department wrote in a document seeking a judge’s permission to seize any weapons in the man’s possession.

The petition said F.B.I. agents reviewed messages between the Wisconsin shooter and the California man. The document did not say how the two communicated, and it did not provide additional details about their correspondence.

The California man does not appear to have been charged with a crime in connection with the shooting. Denise Ramirez, a spokeswoman for the Carlsbad Police Department, said in an email that city officials were helping the F.B.I. in its investigation. She added: “We do not believe there to be a threat to our city.”

Caroline Clancy, a spokeswoman for the F.B.I. in Wisconsin, declined to comment on the agency’s involvement in the investigation.