U.S. President Donald Trump moved aggressively to tighten the nation's immigration policies Wednesday, signing executive actions to jump-start construction of a U.S.-Mexico border wall and block federal grants from immigrant-protecting "sanctuary cities."

"Beginning today the United States of America gets back control of its borders," Trump declared during a visit to the Department of Homeland Security. "We are going to save lives on both sides of the border."

The orders come as the president doubles down on unfounded claims that he lost the popular vote to Democrat Hillary Clinton because of illegal immigrants committing voter fraud.

U.S. to pay upfront cost of wall

While Trump has repeatedly promised that Mexico will pay for the wall, U.S. taxpayers are expected to cover the initial costs and the new administration has said nothing about how it will compel Mexico to reimburse the money.

One of the executive actions Trump signed Wednesday appears to signal that he could restrict aid to Mexico.

Mexican President Enrique Pena Nieto, who has insisted his country will not pay for a wall, is expected to meet with Trump at the White House next week, despite calls from some lawmakers for him to cancel his visit.

Trump signs two executive orders during a visit to the Department of Homeland Security. The orders jump-start the construction of a U.S.-Mexico border wall and end federal funding for so-called sanctuary cities. (Chip Somodevilla/Getty Images)

"The position is very clear," said Ricardo Anaya Cortes, president of the conservative opposition National Action Party. "Either one cancels the meeting with Donald Trump, or one attends it to say publicly and with absolute firmness that Mexico rejects the wall and we will not pay a single cent for it."

Congressional aides say there is about $100 million of unspent appropriations in the Department of Homeland Security account for border security, fencing and infrastructure. That would allow planning efforts to get started, but far more money would have to be appropriated for construction.

Crackdown on sanctuary cities

Trump also signed an order to strip federal grant money from sanctuary states and cities, often governed by Democrats, where local officials refuse to co-operate with federal authorities on actions against undocumented immigrants.

Leaders of sanctuary states and cities appeared undaunted.

Boston Mayor Marty Walsh promised to let immigrants who feel threatened by the administration's actions take shelter in city hall if necessary.

Seattle Mayor Ed Murray said he instructed city departments to rework their budgets to prepare for the possibility that federal dollars could be lost, saying: "This city will not be bullied by this administration."

Washington Gov. Jay Inslee called Trump's order mean-spirited and unnecessary. California Senate president pro tempore Kevin de Leon, an L.A. Democrat, tweeted: "See you in court."

In New York, Trump's hometown, city officials said the administration's action could take away over $150 million in law enforcement funding mainly for counterterrorism efforts, protecting international missions and dignitaries and, arguably, safeguarding Trump Tower, city officials said.

"This order could, in fact, undermine public safety," Democratic Mayor Bill de Blasio said.

'I do have a big heart'

The orders also increase the number of border patrol officers by 5,000, triple the number of Immigration and Customs Enforcement agents, and end what Republicans have labelled a catch-and-release system, wherein some immigrants caught crossing the border illegally are released and given notices to report back to immigration officials at a later date.

Trump told ABC News in an interview broadcast on Wednesday said that illegal immigrants brought to the U.S. as children, known as "dreamers," should not be worried about deportation.

"They shouldn't be very worried," Trump said.

"I do have a big heart. We're going to take care of everybody," Trump said, adding: "Where you have great people that are here that have done a good job, they should be far less worried."

"We'll be coming out with policy on that over the next period of four weeks," he added.

Voter fraud investigation

Trump has blamed illegal immigrants not only for crime, but also for his own failure to secure the popular vote.

Republican Trump won the Electoral College that decides the presidency and gives smaller states more clout in the outcome. However, he lost the popular vote to Democratic rival Clinton by about 2.9 million.

Trump said he would seek a "major investigation" on voter fraud in the November election, despite an overwhelming consensus among state officials, election experts and politicians that voter fraud is rare in the United States.

U.S. President Donald Trump doubled down on his voter fraud claim, tweeting his plans to investigate the issue 2:10

State officials in charge of the Nov. 8 election have said they found no evidence of widespread voter fraud and there is no history of it in U.S. elections.

I will be asking for a major investigation into VOTER FRAUD, including those registered to vote in two states, those who are illegal and.... —@realDonaldTrump

even, those registered to vote who are dead (and many for a long time). Depending on results, we will strengthen up voting procedures! —@realDonaldTrump

'Black site' prisons and Syria safe zones

More executive orders on national security are expected from Trump.

A draft executive order obtained by The Associated Press shows that he intends to stop accepting Syrian refugees and will suspend the United States' broader refugee program for 120 days.

The president also plans to suspend issuing visas for people from Iran, Iraq, Libya, Somalia, Sudan, Syria or Yemen for at least 30 days, according to the draft. All are predominantly Muslim countries.

Another draft order seen by Reuters suggests Trump will have the Pentagon and the State Department craft a plan for setting up "safe zones" for refugees in Syria, move that could risk escalation of U.S. military involvement in Syria's civil war.

Two U.S. officials speaking on condition of anonymity told Reuters that Trump is expected to order a review that could lead to bringing back a CIA program for holding terrorist suspects in secret overseas "black site" prisons where interrogation techniques often condemned as torture were used.

Trump told ABC News Wednesday that torture is an effective tool, adding: "We have to fight fire with fire."