WASHINGTON — Three veterans killed themselves last week on Department of Veterans Affairs health care properties, barely a month after President Trump announced an aggressive task force to address the unremitting problem of veteran suicide.

Mr. Trump’s executive order was a tacit acknowledgment of what the deaths rendered obvious: The department has not made a dent in stemming the approximately 20 suicide deaths every day among veterans, about one and a half times more often than those who have not served in the military, according to the most recent statistics available from the department.

A 2015 measure that required officials to provide annual reviews of mental health care and suicide prevention programs has found that veterans often receive good mental health care at many Department of Veterans Affairs centers — but that has not decreased suicide rates. A relatively new program, known as the Mayor’s Challenge, that helps city and state governments reach more veterans through more public health programs via Veterans Affairs partnerships has shown some promise, but no data exists yet demonstrating suicide reductions.

While the V.A. has been the public face of the issue, veterans are in many ways an amplification of the same factors that drive suicide in the broader American population: a fragmented health care system, a shortage of mental health resources, especially in rural areas, a lack of funding for suicide research and easy access to guns. All of these contribute to the drastically increased suicide rate among all Americans, which rose 33 percent from 1999 to 2017.