Trump tweeted, "Chuck Jones, who is President of United Steelworkers 1999, has done a terrible job representing workers. No wonder companies flee country!"
And about an hour later, Trump tweeted, "If United Steelworkers 1999 was any good, they would have kept those jobs in Indiana. Spend more time working-less time talking. Reduce dues."
Speaking to CNN's Erin Burnett on Wednesday night, Jones responded to Trump, saying, "Well, first of all, that wasn't very damn nice. But with Donald Trump saying that, that must mean I'm doing a good job. Because these people are making a decent wage at Carrier. And I feel like I'm somewhat involved in making that happen. And he does everything he can to keep unions out of his hotels and casinos here in this country, depriving them of making a living wage. So I don't put a whole hell of a lot of faith in whatever he says."
Last week, sources familiar with the deal told ABC News that approximately 800 jobs will stay at the Carrier furnace factory in Indianapolis but that approximately 600 jobs will still move to Mexico. The company will keep 300 white-collar jobs, such as research and headquarters positions, in Indianapolis, but those jobs were never slated to move to Mexico.
Carrier's parent company, United Technologies, also plans to move 700 jobs from the United Technologies Electronic Controls factory in Huntington, Indiana, to Mexico.
During the interview with Burnett, Jones took aim at Trump's claim of saving 1,100 Carrier jobs.
"When Carrier announced the close-down the whole facility in February, they announced at that point in time the research and development jobs, about 350 of them, were going to remain here in Indianapolis," Jones said. "Then when Mr. Trump got involved, what the actual number of jobs saved is 730 bargaining unit jobs, the workers, the union members. And another 70 office, supervisory, clerical workers from management. And what they are doing is counting in 350-some-odd more that were never leaving this country at all. And I think he's did a lot of negotiations, and I have likewise. And if you are dealing with people's livelihoods, you sure in the world ought to know what the numbers are."
And in an interview with CNNMoney earlier that day, Jones was more pointed. "He's lying his a-- off," he said about Trump's claim of saving 1,100 jobs. "That's not just my feeling. The numbers prove he's lying his a-- off. It's a damn shame when you come in and make a false statement like that."
Jones said Trump should be working to prevent the relocation to Mexico from Indianapolis of a plant owned by another company, Rexnord.
"Trump said no companies would be allowed to go to Mexico," Jones said. "There are more than 300 people over there at Rexnord. He needs to deliver for them as well."
ABC News' Arlette Saenz contributed to this report.