"We're not going to allow that to happen any longer," he told a bikers' rally in Washington DC.
Mr Trump did not provide any evidence for his assertion.
Last year, the billionaire sparked anger by attacking the military record of Senator John McCain, a former prisoner of war.
Mr Trump said Sen McCain was only considered a hero because he was a prisoner of war during the Vietnam War.
He then added: "I like people who weren't captured."
