He and first lady Melania observed a solemn moment of silence at the White House and later at the Pentagon.
Thousands are gathering nationwide to mark the deadliest attack on US soil.
Nearly 3,000 people died after hijackers crashed planes into New York's World Trade Center, the Pentagon and a rural Pennsylvania field in 2001.
Mr Trump and the first lady observed a moment of silence at the Pentagon at 09:37 (13:37 GMT), when US officials say American Airlines Flight 77 crashed into the building.
"Our values will endure, our people will thrive, our nation will prevail, and the memory of our loved ones will never, ever die," the president said afterwards.
Mr Trump joined Defence Secretary James Mattis and General Joseph Dunford, chairman of the Joint Chiefs of Staff, at the Department of Defense to remember the lives lost on 9/11.
"The terrorists who attacked us thought they could incite fear and weaken the spirit. Those who try will soon join the long list of vanquished enemies who dare to test our mettle," he said.
The president acknowledged the more than five million young men and women who joined the military since 9/11 to "defend our country against barbaric forces of evil and destruction".
"We are making plain to these savage killers that there is no dark corner beyond our reach, no sanctuary beyond our grasp, and nowhere to hide anywhere on this very large Earth," he continued.
Earlier, Mr Trump appeared at the White House for a commemoration.
Meanwhile, relatives of 9/11 victims, survivors, rescuers and others gathered at New York's 9/11 memorial at 08:46 to mark the exact time the first plane struck the World Trade Center's North Tower.
The second plane slammed into the South Tower at 09:03.
The names of the 3,000 killed were read aloud at the 9/11 Memorial and Museum as bells rang out in memory of the dead.
Each year on the anniversary, two light beams illuminate the sky in place of the two towers.
The fourth plane went down at 10:03 in Shanksville, Pennsylvania, where crew members wrestled hijackers for control of plane, forcing it down in a rural field instead of its intended target in Washington.
Vice-President Mike Pence and Secretary of the Interior Ryan Zinke appeared on Monday in Shanksville, where ground was broken a day before for a 93ft (28m) tower at the Flight 93 National Memorial.
The Tower of Voices will remember the 33 passengers and seven crew members who died on Flight 93.
"They were ordinary people, but on that day they were extraordinary," said Mr Pence.
Photo caption: President Trump was joined by his wife Melania and his daughter Ivanka