Trump said these suicides often occur because veterans are not able to quickly make an appointment for "what could be a simple procedure, a simple prescription".
During the town-hall-style event, a combat veteran asked Trump what he would do to end the "social engineering" in the military, which now allows women and transgender individuals to serve. Trump agreed that the military has become too "politically correct" and said he would follow the recommendations of top military leaders.
"We have a politically correct military, and it's getting more and more politically correct everyday," Trump said.
"And a lot of the great people in this room don't even understand how it's possible to do that. And that's through intelligence, not through ignorance - believe me - because some of the things that they're asking you to do and be politically correct about are ridiculous."
Trump's comments came during his first campaign event since new revelations about his personal taxes, which have drawn intense scrutiny, but he did not mention the New York Times report on Saturday that said he declared a loss of $916 million on his 1995 income tax returns, which could have enabled him to avoid paying federal income taxes for 18 years.
Instead, Trump continued to criticise Hillary Clinton's use of a private email server as secretary of state and laid out his plan to counter the threat of cyberattacks, an issue that came up during the presidential debate last week, although he struggled to provide a clear answer.
"Hillary Clinton's only experience in cybersecurity involved her criminal scheme to violate federal law," said Trump, referencing Clinton's emails. A Justice Department criminal probe of Clinton's email practices resulted in no charges against her.
Trump said the threat of cyberattacks from the governments of countries such as China, North Korea and Russia constitutes "one of our most critical" national security concerns. As president, Trump said, he would promptly commission a review of cyber defenses and weaknesses and ensure that the issue is a high priority.
However, Trump has sent mixed messages about safeguarding against online attacks from foreign intruders. During the summer, he called on Russia to hack Clinton's emails in hopes of recovering the ones that she said were personal and deleted.
"Russia, if you're listening, I hope you're able to find the 30,000 emails that are missing. I think you will probably be rewarded mightily by our press," Trump said in July.
Monday's town-hall-style event in Herndon, Virginia., was hosted by a political action group called Retired American Warriors. Trump gave prepared remarks and then fielded some questions from the friendly audience.
Trump said those who violate rules governing classified information should be prosecuted to the "fullest extent of the law." And he claimed that "lately, we're more interested in protecting the criminals than making sure we're strong and powerful."
Trump added: "I think we need to go back to a little more old-fashioned method of thinking."
With about five weeks left until the election, Trump is trying to recover from a bruising few days. In addition to new attention on his taxes, his performance in the first debate was viewed as weak, polling shows, and he continued to engage in personal feuds that many Republicans deemed counterproductive.
At Monday's event, Trump repeated some positions he has emphasised earlier in his campaign, including the need for authorities to engage in "profiling" to guard against the threat of terrorism. He also railed against political correctness and vowed to protect religious liberty.
