On a local TV program Diaz claimed that by saying Honduras "doesn't do anything" to stop illegal immigration, Trump demonstrates that "he is not well informed".
Earlier on Tuesday Trump took to Twitter to warn Honduras and Mexico that retaliation may follow if a reported caravan of more than 1,000 Central American migrants illegally enters the United States.
"Cash cow NAFTA is in play, as is foreign aid to Honduras and the countries that allow this to happen," the president wrote.
"The causes of immigration are violence, drug violence, drug trafficking. What has President Trump done to reduce the demand for the drugs that enters that market [in the United States] that generates violence in our country?" Diaz said, as cited by Reuters, adding that "Honduras will continue to grow, with or without the support of President Trump."
Although Honduras' murder rate has been falling steadily in recent years, the country remains one of the world's deadliest peacetime nations.