Supporters of Donald Trump have threatened a workers' union boss and his children after he criticised the President-elect for making false claims about a business deal.

Chuck Jones, leader of the 1999 steelworkers union, attracted the President-elect’s attention after he said the billionaire had “lied his ass off” about coming to an agreement that saved 1,100 American jobs at an air conditioning company called Carrier.

Mr Jones said the deal only kept 800 jobs in the US – with hundreds jobs positions relocating to Mexico – and that it was in exchange for $7m (£5.5m) in tax breaks across the next decade.

The union leader has said Mr Trump overstated the job savings of the deal and he had raised the hopes of workers, who would still see their positions shipped out of the country.

Following Mr Jones’ remarks, Mr Trump took to Twitter to criticise him, saying he had “done a terrible job” and that he should “spend more time working" and "less time talking”.

But within an hour of Mr Trump tweeting his remarks, the union boss said he started to receive threatening phone calls.

“You better keep your eye on your kids, we’re coming for you, we know what car you drive, things like that,” he told MSNBC.

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Yet he said was not phased by the harassment, telling the network he had “been doing this job for 30 years, and heard everything from people who want to burn my house down or shoot me.”

He added that he is “not concerned about it and I’m not getting anybody involved. I can deal with people that make stupid statements and move on.”

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Mr Jones also told NBC News he took the President-elect’s remarks as a compliment: “I tried to correct some of his math, and he took exception to it.

“For him to say I'm a horrible labor leader, I take it as a positive because that must mean that we're doing something so people can earn a decent living wage-wise and benefit-wise.”