WASHINGTON — Despite extensive support and counseling programs, as many as 349 U.S. service members committed suicide last year, which would be the highest number since the Department of Defense began keeping detailed statistics in 2001.

According to the Pentagon, 239 military deaths in 2012 have been confirmed as suicides and another 110 are being investigated as probable suicides. The number of suicides in 2011 reached 301; there were 298 the year before.

The statistics on suicides among service members, many of whom had deployed to war zones, included deaths among reserve forces.

Each branch of the service showed an increase. The Army had by far the highest number of suicides and probable suicides — 182, a number that was up from 166 in 2011. The Navy had 60 suicides in 2012 compared with 52 the year before, followed by the Air Force with 59 (up from 51) and the Marine Corps with 48 (up from 32).

For years, the Pentagon has struggled with how to identify service members at risk for suicide and to provide counseling and other services. The Army and Navy have focused on teaching “resiliency” to troops in hopes of helping them cope with stress. Military experts have long said one of the enduring challenges is that there doesn’t appear to be a direct link between suicides and the stress of being in the combat zone.

A private-sector group, the Tragedy Assistance Program for Survivors (TAPS), which provides military grief support programs, reported it has eight to 10 cases a week of people seeking help because they are dealing with the suicide of a service member. Of the people contacting the organization for care and support, 18% were “grieving a death by suicide,” TAPS said in a statement.

“We are deeply saddened by this loss of life, and renew our commitment to support the military families left behind who are grieving the deaths of service members by suicide,” said Bonnie Carroll, founder of TAPS. She is a former co-chair of a congressionally mandated Department of Defense Task Force on the Prevention of Suicide in the Armed Forces.

“We know that at least 10 people are personally impacted by each death and every death is a tragedy,” Carroll said in the statement.

Kim Ruocco directs suicide postvention programs, counseling and support efforts for people affected by a loved one’s suicide, for TAPS. She said service members in distress deserve “an immediate and comprehensive response.”

“We do not expect for a soldier with a broken leg to be strong and get up and become better without seeking medical treatment,” said Ruocco, the widow of Marine Maj. John Ruocco, who died by suicide in 2005. “When a soldier is suffering from a mental health injury, he or she deserves medical treatment and the very best care that is available.”