Jones bashed Trump on national media outlets for saying his agreement with the United Technologies unit saved more jobs in Indiana than it actually did. Trump announced last week that the agreement — which gives Carrier $7 million in financial incentives — would keep 1,100 jobs in Indiana. Those jobs had been slated to move to Mexico.

"What I did was trying to get the people to understand that the numbers that Mr. Trump and Governor [Mike] Pence made weren't accurate. … I stand behind all" of the remarks, said Chuck Jones, president of United Steelworkers Local 1999.

An Indiana union leader whose criticism of Donald Trump 's Carrier jobs deal prompted a Twitter attack from the president-elect told CNBC on Thursday he does not regret what his words.

Jones said that he then was told the deal would only save about 800 jobs, 730 in production at the Indianapolis plant, and 550 of his members would lose their jobs. He told The Washington Post that Trump "lied his a-- off" about the number of positions the agreement preserved.

A Carrier spokeswoman previously confirmed to CNBC that 300 headquarters and engineering jobs in the state were never getting relocated and were included in the 1,100 position estimate.

Shortly after Jones criticized Trump on Wednesday night on CNN, Trump tweeted that the union leader has done a "terrible job" representing workers. The president-elect added that the jobs would have stayed in Indiana "if United Steelworkers 1999 was any good."

Some have criticized Jones for going after Trump even though his deal saved 800 jobs.

The union boss stressed that he is "grateful" for the president-elect's intervention to keep some positions in Indiana. But he said he rebuked Trump because the higher number that Trump publicly shared gave some workers "false hope" that they would keep their positions.

"I took exception to that because our people, at that time, got their hopes back up that they might have a job. During his interviews, and during his speeches at Carrier, he did not allude to any of that," Jones said. "And people thought there was a good chance that they were going to have a job, be able to provide for their families moving forward, in order to find out Friday, when we told them, 'No, 550 people's jobs are going to Monterrey, Mexico."

Jones, whose local also represents Indiana workers at Rexnord, added that he does not think his criticism of Trump limits his ability to negotiate in the future, saying he believes he can still work with Trump.

Rexnord of Indiana is moving to Mexico and rather viciously firing all of its 300 workers. This is happening all over our country. No more!

