No one has been injured so far in four shootings this month in northern Virginia that have targeted the Pentagon, a marine recruiting office and the National Museum of the Marine Corps, which came under fire for a second time overnight.

The shooter appeared to be trying to "avoid casualties" by opening fire on unoccupied buildings after business hours, John Perren, acting assistant director of the FBI Washington field office, told reporters.

But there was a risk the spree could "lead to disastrous consequences that we all wish to avoid," he said.

Investigators assumed the shooter was either in the marines or a former member of the corps, officials said at the news conference in Washington.

"We believe the subject has a grievance surrounding the US Marine corps. It may be that he feels he's been wronged by the corps in his professional and/or his personal life," he said.

The FBI used the televised press conference to try to send a message to the suspected shooter, asking him to contact authorities and offering to hear him out.

"We'd like to know what this grievance is and what we can do to try to help resolve it. We're willing to listen to him and hear his side of the story."

The suspect likely had suffered recently from a "personal crisis," he said.

The recent shootings prompted the Defense Department to tighten security before this Sunday's US Marine Corps marathon, which is staged at the Pentagon.

But defense officials said the race would go ahead as scheduled, despite the spate of shootings that appeared to single out the marine corps.

The Federal Bureau of Investigation on Thursday had confirmed a clear link to the first three shootings after carrying out ballistic tests on bullets found at the sites.

The attack overnight at the Marines' museum was under investigation but FBI officials said they were proceeding with the assumption that it was also carried out by the same gunman with the same weapon.

Several shots were fired late Thursday or early Friday at the museum in Triangle, Virginia, south of Washington, First Sergeant Kim Chinn of the Prince William County police told AFP.

The museum was first shot at on October 17, and shots were fired at the Pentagon on October 19. A marine recruiting station came under fire earlier this week.

Security has been steadily bolstered in recent months at the Pentagon in the aftermath of an attack by an American gunman in March, who walked up to the main entrance and opened fire, wounding two police officers before he was shot dead by return fire.

The sprawling Defense Department headquarters, just across the river from central Washington, has been heavily guarded since the attacks of September 11, 2001, when a hijacked plane slammed into the building.

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