Mr Trump built much of his campaign on his promises to tackle immigration and border control. During his campaign for the White House, he repeatedly promised to build a border wall, and make Mexico pay for it.
He told CBS television he will accept a fence instead of a wall, for certain areas of the border, although he said a wall was more appropriate for other regions.
In his first television interview since winning the presidential election, Mr Trump insisted he would carry out his hardline immigration proposals.
"What we are going to do is get the people that are criminal and have criminal records - gang members, drug dealers, we've a lot of these people, probably two million or maybe three million - we're getting them out of our country or we're going to incarcerate but we're getting them out of our country if they're here illegally.
Mr Trump has also asked for his fraud trial to be delayed until after he is sworn in early next year.
Former students of Mr Trump's failed Trump University are suing him, saying they were duped into paying up to $35,000 each for fraudulent courses promising to teach them his real estate investing secrets.
He caused controversy during the election campaign, by saying the judge in the trial could not be impartial because he is of Mexican descent.
Mr Trump's lawyer filed a motion asking for a delay, saying the president-elect needED to devote all his time and energy to the transition to the White House.
The president-elect denies the fraud allegations and said he relied on others to manage the business.
Meanwhile, a Chinese diplomat said the country was ready to improve relations with the United States Mr Trump's election as the next president.
Mr Trump has taken a tough stance on China, blaming it for a widespread decline in US manufacturing.
But on a visit to Turkey, Chinese foreign minister Wang Yi said his country was looking to improve its ties with the US.