"Let's get a pull-up bar out there and let's see who can do the most pull-ups," said Perry, once an Air Force captain, when asked by a reporter if he had any message for Trump.
Perry, who governed Texas with a trademark swagger and bravado for 14 years, made the remark after a speech dedicated to Wall Street reform at the Yale Club in New York on Wednesday.
Perry has emerged as one of the fiercest critics of Trump, who currently leads polling in the Republican field, even calling for the real estate mogul to drop out of the race.
Trump has returned fire, questioning Perry's ability to secure the border as governor and saying that he doesn't have the intelligence required to for the presidency.
Perry and his aides have needled Trump for what they see as a mismatch between his tough talk and his tony, cosmopolitan image. On Wednesday, Perry's senior strategist in Iowa, Bob Haus, used Twitter to note what Trump wore when he visited the Texas-Mexico border earlier this month.
"This is what a Manhattan 'tough guy' wears to the southern border," Haus tweeted. "White golf shoes and a linen jacket."