WASHINGTON — The deadly shootings at military sites in Tennessee illustrate the threat that FBI officials have warned about: violence directed against a vulnerable government target by a lone gunman with apparent terrorist aspirations.

The FBI has not detailed a motive, but Thursday’s attacks that killed four Marines and one sailor are under investigation as a potential act of terrorism, with authorities combing through the gunman’s past to look for travel, contacts and online writings.

The rampage unfolded as the federal government has raised alarms about the online spread of terrorist propaganda, including repeated exhortations by groups such as the Islamic State for sympathizers to target police officers and military installations.

It came two months after two men opened fire outside a Prophet Mohammed cartoon contest in Texas before being killed by police, and during a year when several dozen people in the United States have been charged with supporting terrorism, with more than 10 arrested in the month before the July 4 holiday.

“This is the new normal,” said Will McCants, a terrorism expert at the Brookings Institution in Washington. If a terrorist group is looking to influence public opinion and generate fear, he said, “this kind of tactic has a lot going for it.”