The new Republican president is expected to sign several executive orders on immigration and border security this week.
They are likely to include the "extreme vetting" of people coming from seven predominantly Muslim countries in the Middle East and Africa.
This would restrict refugee access.
Mr Trump tweeted: "Big day planned on national security tomorrow. Among many other things, we will build the wall!"
Meanwhile, the Dow Jones traded above 20,000 for the first time, as traders bet that Mr Trump's policies will boost the economy.
Building a 2,000-mile wall along the Mexican border was one of his key proposals during the presidential election campaign.
During his election campaign, Mr Trump said Mexico would pay for the wall, which he said would cost about $8bn (£6.4bn).
He has since said the US would recoup the costs from its neighbour at a later date.
But Mexico's president and senior officials have said that they will not pay for the wall, despite Mr Trump's campaign pledge.
There will also be measures that force so-called sanctuary cities in the US to co-operate with the authorities on deporting illegal immigrants.
"Sanctuary cities" are places that don't arrest or detain immigrants living in the country illegally.
Meanwhile, a draft White House order raises the possibility that overseas "black site" CIA-run prisons could be reopened.
The document asks senior national security officials whether the president should "reinitiate a program of interrogation of high-value alien terrorists to be operated outside the United States".
The order, obtained by the Associated Press, says US laws should be obeyed at all times and explicitly rejects "torture".
Later this week, Mr Trump is expected to announce immigration restrictions from seven African and Middle Eastern countries, including Syria, Yemen, and Iraq.
He is also likely to halt access to the country for some refugees - until the vetting process can be made more rigorous.
Trita Parsi, from the National Iranian American Council, said: "He called for a Muslim ban and is now taking the first steps to implement one. This will not stand. The American people are better than this."
But one of Mr Trump's advisers on the transition team at the Department of Homeland Security, James Carafano, said the new measures should not be seen as anti-Muslim.
<>p"If they're based on security concerns, of course they have nothing to do with a person's actual religion, it's based on that they're conflict zones or that there are security concerns coming out of that country," said Mr Carafano, who is from the conservative think-tank the Heritage Foundation in Washington.Meanwhile, Mr Trump has promised a "major investigation into voter fraud", after making claims about millions of illegal ballots.
The new president said the inquiry would include "those registered to vote in two states, those who are illegal".
Mr Trump also said the probe would focus on "those registered to vote who are dead (and many for a long time)".
He has claimed that up to five million illegal votes were cast for Hillary Clinton but has offered no evidence.
The US president has also taken to Twitter to express his concern about the level of violence in Chicago.
He threatened to "send in the Feds" - federal authorities - if the city did not "fix the horrible carnage" taking place.
Local media has said that more than 40 people have been murdered and 228 shot so far in 2017.
The Chicago Police Department said it was "more than willing to work" with federal agencies to "boost federal prosecution rates for gun crimes" in the city.
Meanwhile, the Dutch government has said it will set up an international fund to counter the effects of Mr Trump's ban on US funding for abortions in developing countries.
<>The Dutch development minister, Lilianne Ploumen, said withdrawing funding would not result in fewer abortions, but would increase dangerous abortion practices and cause more maternal deaths.
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