"This will stem the flow of drugs, crime and illegal immigration into the United States," Spicer added.
"And yes, one way or the other, as President Trump has said, Mexico will pay for it," he added.
A second executive order was focused on ensuring the full enforcement of existing immigration laws, as the Trump Administration will end what's known as "catch and release" of illegal aliens.
The plan would also seek to block federal funding that goes to so-called sanctuary cities in the U.S., where governments do not help the feds arrest or detain illegal immigrants.
"Federal agencies are going to uanpologetically enforce the laws, no ifs, ands or buts," said Spicer.
One thing that was not acted on by the President was any change in President Obama's immigration actions related to DACA, the program that allows younger people brought to the U.S. illegally by their parents to stay here, without the threat of deportation.
Spicer said again today that DACA could be dealt with at a later date.
Opponents of illegal immigration hailed the President's moves.
"President Trump’s executive actions are an historic, much-needed course correction in America’s approach to immigration policy, which has been on autopilot for decades," said Dan Stein, the head of the Federation for American Immigration Reform.
"For the past eight years, our country suffered under the Obama Administration’s lax enforcement of immigration laws," said Rep. Robert Goodlatte (R-VA).
Democrats were not impressed.
"Donald Trump's executive orders are an attack on immigrant communities," said Rep. Rosa DeLauro (D-CT).
"Congress should pass comprehensive immigration reform, not build a wall of hate," said Rep. Steny Hoyer (D-MD).
Here are the full details of the two Trump orders related to immigration: