WASHINGTON — Defense Secretary Chuck Hagel said Wednesday the military missed “red flags” in Washington Navy Yard shooter Aaron Alexis’s background, pledging to fix any holes in security clearance procedures.

“Where there are gaps, we will close them; where there are inadequacies, we will address them; and where there are failures, we will correct them,” Hagel told reporters at the Pentagon. He announced separate reviews, by the Defense Department and an independent panel, of security at military facilities worldwide and the clearance process.

Alexis, 34, was a contractor who entered the Naval Sea Systems Command headquarters Sept. 16 with a valid pass and had a secret clearance, despite having an arrest record, troubled military career and history of mental illness.

“Obviously, when you go back in hindsight and look at all of this, there were some red flags — of course there were,” Hagel said. “Should we have picked them up? Why didn’t we? How could we? All those questions need to be answered.”

In New York, Alexis’s mother released a brief statement apologizing to the families of her son’s victims, saying she was heartbroken.

“I don’t know why he did what he did, and I’ll never be able to ask him why,” Cathleen Alexis said in the statement, according to audio posted by NBC News on its website. “Aaron is now in a place where he can no longer do harm to anyone, and for that I am glad.”

While Alexis was involved in a series of run-ins with law enforcement before this week’s carnage, none is known to have led to a criminal conviction or serious legal consequences.

At the Pentagon, Gen. Martin Dempsey, chairman of the Joint Chiefs of Staff, said military personnel who suffer from mental health issues should be encouraged to seek help without being “stigmatized,” and said even the tightest security checks may not have been able to predict this week’s horror.

“He committed murder,” Dempsey said of Alexis. “I’m not sure that any particular question or lack of question on a security clearance would probably have revealed that.”

Warning signs were surfacing as recently as a few weeks before this week’s rampage at the Navy Yard in southeast Washington.

Alexis called police to a Newport, R.I., hotel room early Aug. 7 to report that he believed three people had been sent “to follow him and keep him awake by talking to him and sending vibrations into his body,” according to a police incident report. He told the responding officers he was a naval contractor and said he thought the people had been sent to harass him by a stranger with whom he’d argued.

Because of the voices, Alexis said, he had switched hotels three times — at one point checking into one on a Navy base. He said he continued to hear the voices, telling police he was afraid he would be harmed by the people, who he said were using “some sort of microwave machine” to send vibrations to penetrate his body.

Alexis “stated that he does not have a history of mental illness in his family and that he has never had any sort of mental episode,” the responding officer wrote in the report.

An officer who approved the incident report was concerned enough about the episode and Alexis’s stated connection to the Navy to notify the Naval Station Police, he wrote in a subsequent report.

“Based on the Naval Base implications” and Alexis’s claim that he was “hearing voices,” that officer wrote, he contacted on-duty Naval Station Police personnel and faxed over a copy of the incident report.

The second report indicates that the Naval Station individual who was contacted, whose name wasn’t released, told the officer that he or she “would follow up on this subject and determine if he is in fact a naval base contractor.”

A public affairs officer at Naval Station Newport referred questions to the FBI. Jacqueline Maguire, an FBI spokeswoman, said the agency was aware of the police report.

“It is part of our investigation to track back and look at Mr. Alexis’ past, his history, his activities,” Maguire said in an interview. She declined to comment on whether information about the police report was pursued at the time.

The Newport episode was one in a series of run-ins Alexis had with police — including gun-related incidents in Forth Worth, Texas, and Seattle that didn’t lead to convictions.

In 2010, Fort Worth police arrested Alexis after an upstairs neighbor who said she was “terrified” of Alexis reported that a bullet came through her floor from his apartment below, missing her by only feet.

Alexis told officers he was cleaning a gun when it went off, according to police records, and Tarrant County authorities believed him, declining to charge him with recklessly discharging a firearm.

In 2004, Alexis was arrested in Seattle for shooting the tires on a car belonging to a construction worker parked near where he lived, according to an incident report posted by city police. Alexis told police that he’d shot his gun during a “blackout” fueled by anger, after he believed the construction worker had mocked and disrespected him.

Alexis also told the arresting officer he had been “disturbed” by the Sept. 11 terrorist attacks and, in a subsequent interview, his father told authorities his son had “anger-management problems” the family thought stemmed from stress following his involvement in post-9/11 rescue efforts.

Charges in the Seattle incident were never pursued, for reasons that aren’t clear to law enforcement authorities there.

Kimberly Mills, a spokeswoman for the Seattle city attorney, said the police report — which contained allegations of property destruction and discharge of a firearm — “did not get to our office — unknown why — and thus it was not considered for charges.”

In 2008, Alexis was arrested for disorderly conduct in DeKalb County, Georgia, and spent two nights in jail after being ejected from a local club, WGCL Television in Atlanta reported.

Scrutiny of military security came as law enforcement officials released more details on the shooting.

Authorities believe Alexis entered the Navy Yard on the morning of Sept. 16 with a shotgun he had purchased legally in Virginia, according to Valerie Parlave, assistant FBI director in charge of the Washington field office. He also may have gained access to a handgun after he began shooting inside the facility, she said.

Officers entered the building where Alexis was within seven minutes and engaged him multiple times before he was shot to death, Washington Police Chief Cathy Lanier said.

Alexis, who was born in New York City, enlisted in 2007 and was last assigned to a logistics support squadron in Fort Worth, according to the Navy. He was granted his secret-level clearance in March 2008, according to a defense official.

While in the Navy, he was reprimanded at least eight times for misconduct, including extended, unauthorized absences, according to another defense official.

He asked to leave the Navy and was honorably discharged in January 2011 because the Navy wanted him to separate from the service, according to a Navy official. The officials asked not to be identified discussing personnel matters.

After departing the Navy, Alexis retained his clearance, which was good for 10 years, and wasn’t subject to a reinvestigation, one of the defense officials said.

The Pentagon’s inspector general released a report yesterday documenting lapses that allowed 52 convicted felons routine access to naval bases.

Alexis had a history of mental illness, which was first revealed during interviews with family members in New York, according to a law enforcement official briefed on the case who wasn’t authorized to speak publicly.

“It really is hard to believe that someone with a record as checkered as this man could conceivably get clearance, could get credentials, to be able to get on the base,” Washington Mayor Vincent Gray said during an interview yesterday with CNN.

At the time of the shooting, Alexis was employed by a subcontractor of Hewlett-Packard Co., on a contract to upgrade equipment on the Navy Marine Corps Intranet network, according to a statement by Michael Thacker, a Hewlett-Packard spokesman.