REUTERS/Andy Clark
Speaking at an event in Iowa, Trump argued that McCain - who has spoken out against Trump for his controversial comments about Mexican immigrants - was not a real war hero.
"He's a war hero because he was captured. I like people that weren't captured," Trump said.
"Perhaps he's a war hero, but right now, he's said bad things about a lot of people,' Trump added.
The real-estate mogul also said that he didn't like McCain after his loss to President Barack Obama in the 2008 presidential election.
"I never liked him after that, because I don't like losers," Trump said.
Trump has recently spoken out more forcefully against McCain, after the veteran senator denounced Trump for "firing up the crazies" during a speech last week in Phoenix.
In response, Trump demanded an apology, and tweeted that McCain is a "dummy."
As the Washington Post reported, Trump is lobbying for a primary challenger to run against McCain in 2016.
Several Republican presidential candidates were quick to condemn Trump.
John McCain is an American hero. I have nothing but respect for his service to our country.
- Gov. Bobby Jindal (@BobbyJindal) July 18, 2015
.@SenJohnMcCain is an American hero & all POW's deserve our nation's highest debt of gratitude. @realDonaldTrump's comments are disgraceful.
- Rick Perry (@GovernorPerry) July 18, 2015