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President-elect Donald Trump has warned companies of "consequences" if they leave the United States.

He was speaking in Indiana, where he took credit for saving 1,000 jobs at the air-conditioning company Carrier Corp, which planned to move to Mexico.

Mr Trump is now in Ohio to begin a "USA Thank You Tour 2016" for his supporters.

During a rally in Cincinnati, he announced he had chosen retired general James Mattis as his defence secretary.

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Mr Trump hailed his negotiations with Carrier Corp as a model for how he would work with other US businesses thinking of moving their jobs abroad.

"We are going to have a situation where they are going to know, number one, we're going to treat them well and, number two, there will be consequences," he said.

"They will be taxed very heavily at the border if they want to leave."

He also reiterated his promise to cut business taxes and regulations in the US.

Carrier Corp has been promised a $7m (£5.5m) package of tax breaks over 10 years in exchange for reportedly saving 800 union workers whose jobs would have been outsourced to Mexico and an additional 300 research and headquarters positions.

An estimated 1,300 jobs will still move south of the border. The $7m tax incentive is contingent "upon factors including employment, job retention and capital investment", according to a Carrier statement.

In addition to the tax break, Carrier and its parent company, United Technologies, have agreed to invest $16m to keep the plant updated, Mr Trump confirmed.

Mr Trump had vowed on the campaign trail to stop American jobs from moving overseas, but said he did not realise he had made the promise to Carrier workers until he watched an interview with one of the company employees on a news programme.

The employee said Mr Trump had pledged to keep jobs from moving to Mexico, which prompted the president-elect to contact the company.

Earlier on Thursday, former Democratic presidential candidate Bernie Sanders criticised the Carrier deal as a reversal on Mr Trump's campaign promise to save all the jobs.

The Vermont Senator penned a , saying Mr Trump had endangered jobs by signalling "to every corporation in America that they can threaten to offshore jobs in exchange for business-friendly tax benefits and incentives".

The president-elect was speaking at a rally at US Bank Arena in Cincinnati, Ohio - the first of several stops on his victory lap.

It is the same venue where Mr Trump drew crowds of 15,000 people at a raucous rally on the campaign trail in late October.

He is expected to hold similar events in key battleground states like Iowa, Pennsylvania, Florida, North Carolina and Michigan in the coming weeks.