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8 year oldThose targeted would be migrants with criminal records, such as gang members and drug dealers, he told US broadcaster CBS in an interview.
He also confirmed that another election promise, to build a wall with Mexico, still stood but could include fencing.
The Republican defeated Democrat Hillary Clinton in Tuesday's presidential vote.
His victory shocked many who had expected Mrs Clinton to win following favourable opinion polls.
Mr Trump is due to take over at the White House on 20 January, when Barack Obama steps down after two terms in office.
Both houses of Congress are also under Republican control.
For the first time since winning the US presidency, Donald Trump has put a number on how many people he plans to deport from US soil and it's a big one - two to three million.
Although he says this group is comprised of violent criminals, drug-dealers and gang members, to hit such a high mark would involve either casting a very wide net that covers even the smallest infractions or also deporting legal alien residents of the US with criminal convictions.
To pull this off, an expanded "deportation force" would almost certainly be necessary, but Mr Trump's advisers have spent the past few days downplaying the prospect of such an organisation.
Meanwhile, Mr Trump also has curtailed the scope of his "big, beautiful" border wall, acknowledging that it could be a fence in some areas. All of this is evidence that Mr Trump is grappling with exactly how to make his controversial immigration promises a reality.
Proposing a multi-billion-dollar wall and mass deportations is easy. Delivering, in the face of fiscal realities and opposition within one's own party, is a different matter entirely.
There are around 11 million undocumented immigrants in the US, many of them from Mexico.
Mr Trump pledged during the election campaign to overturn amnesties introduced by President Obama, and strictly enforce immigration laws, deporting those without correct documents.
In his first major interview to a US broadcaster since the election, Mr Trump told CBS: "What we are going to do is get the people that are criminal and have criminal records, gang members, drug dealers, where a lot of these people, probably two million, it could be even three million, we are getting them out of our country or we are going to incarcerate."
Asked about his plans for the Mexican border, he said "a wall is more appropriate" in some parts but "there could be some fencing",
Other undocumented migrants would be assessed once the border was secured, Mr Trump added.
However, another top Republican, House Speaker Paul Ryan, said on Sunday that border security was a greater priority than mass deportation.
"We are not planning on erecting a deportation force,'' he told CNN's State of the Union programme. "I think we should put people's minds at ease."
How realistic is Donald Trump's Mexico wall?
Forcing Mexico to pay for a border wall became a rallying cry among Trump supporters during the campaign.
Their candidate caused outrage by suggesting Mexicans were exporting "their rapists" to the US, along with drugs and other crime.
In another development, Nato Secretary General Jens Stoltenberg warned Mr Trump that "going it alone" was not an option for Europe or the US.
He said the West faced its greatest security challenge in a generation.
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