US President Donald Trump has laid out his plans for his first term in a speech at the GOP retreat in Philadelphia, promising better trade deals and outlining his intentions for a wall on the southern border.

The Republican stressed the wall would be built and insisted Mexico would bear the cost of the structure, despite repeated protests from President Enrique Pena Nieto that this would not be the case.

"Border security is a serious, serious national issue and problem," he said.

"Most illegal immigration is coming from our southern border. I've said many times that the American people will not pay for the wall and I've made that clear to the government of Mexico.

"Nafta has been a terrible deal, a total disaster for the United States from its inception, costing us as much as $60bn (£47.6bn) a year with Mexico alone in trade deficits."

He added: "On top of that are the trillions of dollars US taxpayers have spent to pay the cost of illegal immigration – much of it is then being sent back and much of it goes back to other countries and often times because they don't respect us the other countries will not accept the criminals that we send back to them that are illegally in our countries.

"I promise you they will start accepting them again quickly – we are not going to have them any longer."

Trump stressed he and Mexican President Enrique Pena Nieto had agreed to cancel their planned meeting for next week – despite Pena Nieto tweeting earlier in the day he had called the White House to cancel the meeting.

The president also stressed the "America first" agenda he spoke of during his inauguration, and outlined the executive orders he had signed in his first few days in office.

"Since taking office I have taken major contractual steps to restore the rule of law and return power to everyday Americans," he said.

"We have issued executive orders to build the keystone and Dakota pipelines and issued a new requirement for American pipelines to be made with American steel and fabricated in the United States."

Trump also mentioned reinstating the Mexico City policy that will limit access to abortions for women around he world, and took the opportunity to have a dig at the media, in an ongoing battle between his administration and the mainstream press.

"We have reinstated the Mexico City policy, a longstanding policy, " he said to wide applause from the GOP retreat. "Isn't that nice. And by the way on Friday a lot of people are going to be showing up to Washington, you know the press never gives them the credit that they deserve they will have 300, 400, 500, 600,000 people – you won't even read about it.

"When other people show up you read big time about it, right, so it's not fair but nothing fair about the media. Nothing."

The Trump administration's take on "alternative facts" and insistence the media have incorrectly reported on the president is causing concern among the press, particularly given the recent news that Trump has ordered some government departments to stop communicating with the media and the public.