President-elect Donald Trump has criticised Boeing for the cost of a new Air Force One plane, calling for the contract to be cancelled.

"Boeing is building a brand new 747 Air Force One for future presidents, but costs are out of control, more than $US4 billion ($5.3 billion). Cancel order!" Mr Trump tweeted.

Shortly after the tweet, he made a surprise appearance in Trump Tower in New York before a group of reporters.

"The plane is totally out of control. I think it's ridiculous. I think Boeing is doing a little bit of a number. We want Boeing to make a lot of money but not that much money," Trump said.

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Following the comments, shares in Boeing fell by more than one per cent in the first minutes of trading, making it one of the biggest losers on the Dow Jones to open the day. Just prior to the tweet, the stock was trading unchanged.

The Pentagon announced in January that Boeing had won the contract to replace the current air force One planes. The initial contract was worth just $25.8 million, but the air force planned on spending as much as $1.65 billion on the project, according to Reuters.

In a statement, Boeing said it was under a $170 million contract to work on Air Force One.

"We are currently under contract for $170 million to help determine the capabilities of these complex military aircraft that serve the unique requirements of the President of the United States," the statement said.

"We look forward to working with the US air force on subsequent phases of the program allowing us to deliver the best planes for the President at the best value for the American taxpayer."

The White House said the statistics cited by Trump on Air Force One "do not appear to reflect arrangements" between Boeing and the Department of Defence.

Boeing has supplied planes to the Air Force One fleet for nearly 50 years.