WASHINGTON—A man was in custody here Wednesday after allegedly shooting a security guard at the Family Research Council, a conservative group known for its opposition to gay marriage and abortion.

The suspect, identified by the Federal Bureau of Investigation as 28-year-old Floyd Corkins of Herndon, Va., allegedly approached the building around 10:50 a.m., walking under the entrance's stone façade, which reads, "Faith. Family. Freedom."

Authorities said Mr. Corkins tried to enter the council's offices but was stopped in the lobby by the security guard. The suspect then allegedly fired a gun at the guard, wounding him in the arm. District of Columbia Police Chief Cathy Lanier said the guard and others managed to subdue and disarm the gunman. The guard's injury isn't considered life-threatening.

Late Wednesday, the FBI said the suspect would be charged with assault with a deadly weapon.

Investigators were trying to determine whether he is mentally ill, and if the motive for the alleged attack might fall under the legal definitions of domestic terrorism, a hate crime or something else, law-enforcement officials said. Mr. Corkins couldn't be reached for comment.