The union boss who slammed Donald Trump for "lying his ass off" over the Carrier jobs deal has received threatening calls after a series of tweets by the president-elect.

Chuck Jones, whose union United Steelworkers 1999 represents employees at air-conditioning company Carrier, was criticised in a tweet by Trump following comments that the deal to keep 1,000 jobs in Indiana was not as the Republican had promised.

Trump wrote: "Chuck Jones, who is President of United Steelworkers 1999, has done a terrible job representing workers. No wonder companies flee country!

"If United Steelworkers 1999 was any good, they would have kept those jobs in Indiana. Spend more time working-less time talking. Reduce dues."

Following the tweets, Jones told MSNBC he had received a number of threatening phone calls.

"Nothing that says they're going to kill me, but, you know, you better keep your eye on your kids," Jones said.

"I've been doing this job for 30 years, and I've heard everything from people who want to burn my house down or shoot me.

"So I take it with a grain of salt and I don't put a lot of faith in that, and I'm not concerned about it and I'm not getting anybody involved. I can deal with people that make stupid statements and move on."

Donald Trump
US President-Elect Donald Trump speaks at an event at Carrier HVAC plant in Indianapolis, Indiana, US 1 December 2016. REUTERS/Chris Bergin

Of the 1,100 jobs Trump pledged to save, just 730 production jobs in Indiana were preserved, leaving more than 500 people without work, Jones claimed.

Jones said the president-elect had not offered an explanation at a 1 December speech at the factory, in which Trump had said: "Now they're keeping — actually the number's over 1,100 people, which is so great,"The Washington Post reported.

It was a figure Jones claims misrepresented the situation, telling the newspaper: "He got up there and, for whatever reason, lied his ass off."