Three men charged Tuesday with illegally possessing a machine gun are suspected of bombing a mosque in Minnesota and attempting to bomb an abortion clinic in Illinois last year, federal officials said.

While the complaint does not charge the men with crimes related to the bombing episodes, the authorities said that they had gathered evidence indicating that the men were responsible for them. The investigation is continuing, they said.

One of the men, Michael McWhorter, admitted to the police that he participated in the bombing in Bloomington, Minn., on Aug. 5 and the attempted bombing in Illinois on Nov. 7, a federal affidavit said. Mr. McWhorter said that he and the two other men involved did not intend to kill anyone, but had chosen to bomb the mosque to “scare” Muslims “out of the country” and to signal that they were “not welcome here,” according to the affidavit.

The men — Mr. McWhorter, 29, Michael B. Hari, 47, and Joe Morris, 22 — believed that Muslims “push their beliefs on everyone else,” the affidavit said. It was unclear whether the men had lawyers.