President Donald Trump has warned business leaders he will impose a "substantial border tax" on companies that move their manufacturing out of the United States, while promising tax advantages to companies that produce products domestically.

"All you have to do is stay," he said during a morning meeting in the White House's Roosevelt Room.

Tesla chief executive Elon Musk and Marillyn Hewson of Lockheed Martin were among the executives who attended the meeting.

The gathering kicked off a jam-packed day for the new president, including an evening reception with politicians from both parties and a sit-down with union leaders. The president also planned to sign multiple executive orders in the Oval Office.

Mr Trump had pledged to quickly use his executive authority to withdraw the US from the 12-nation Trans-Pacific Partnership trade pact agreed to under the Obama administration.

He is also expected to sign an order implementing a federal government hiring freeze.

Conservatives are also eager for Mr Trump to sign an order reinstating a ban on providing federal money to international groups that perform abortions or provide information on the option.

The regulation, known as the Mexico City Policy or, by critics, the "global gag rule", has been a political volleyball, instituted by Republican administrations and rescinded by Democratic ones since 1984.

Mr Trump ran for office pledging to overhaul US trade policy, arguing massive free-trade agreements have disadvantaged American workers.

Since winning the White House, he has aggressively criticised companies that have moved factories overseas, vowing to slap taxes on products they then try to sell in the US.

"Some people say that's not free trade, but we don't have free trade now," Mr Trump said today.

The president also reiterated his campaign pledge to lower taxes for companies, as well as the middle class, "anywhere from 15 to 25 per cent".

He also called for cutting 75 per cent of regulations, though he insisted that doing so would not compromise worker safety.

Mr Trump's outreach effort comes after a tumultuous first weekend in the White House that included lambasting news organisations for correctly reporting on the size of the crowds at his inauguration and mass protests against his presidency on the following day.

Mr Trump delivered a more unifying message on Sunday and sought to reassure Americans he was up to the daunting task ahead.

Speaking in the White House East Room during a swearing-in ceremony for top aides, the president warned his staff of the challenges ahead but declared he believed they were ready.

"But with the faith in each other and the faith in God, we will get the job done," he said.

"We will prove worthy of this moment in history. And I think it may very well be a great moment in history."

Mr Trump said his staff were in the White House not to "help ourselves" but to "devote ourselves to the national good".

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