US firms that relocate abroad will be punished under Donald Trump's administration, the president-elect warned Thursday as he announced a deal with air conditioning manufacturer Carrier to keep jobs in the country.

"Companies are not going to leave the United States any more without consequences. Not going to happen," Trump told workers at the Carrier plant in Indianapolis in his first major public remarks since winning the White House.

"They can leave from state to state, and negotiate deals with different states, but leaving the country will be very, very difficult," Trump added.