Immigrant advocates quickly denounced the administration's move.
The issue of the country's loose asylum laws - where foreign nationals can claim that they fear for their lives in their native country and be released into the US until their day in court - has sparked debate as a caravan of 7,000 to 10,000 Central Americans heads to the U.S.
The new rule is nearly certain to be challenged in courts.
Immigrant advocates have denounced the move, saying it violated existing USA law that allows people fleeing persecution and violence in their home countries to apply for asylum regardless of whether they enter illegally or not.
The new rules are subject to a presidential proclamation expected Friday in which Trump will invoke the same justification he did for the travel ban. "It is illegal to circumvent that by agency or presidential decree", Omar Jadwat, director of the American Civil Liberties Rights Project, said.
The rule, which prevents migrants from claiming asylum if they do not do so at an official border crossing, is the latest attempt by the White House to handle a surge in migration to the US from the Central American countries of Guatemala, Honduras and El Salvador.
'Our asylum system is overwhelmed with too many meritless asylum claims from aliens who place a tremendous burden on our resources, preventing us from being able to expeditiously grant asylum to those who truly deserve it, ' Department of Homeland Security Secretary Kirstjen Nielsen and Acting Attorney General Matthew Whitaker said in a joint statement.
Administration officials have said existing United States asylum rules encouraged illegal immigration and bogged down legitimate claims.
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Others held signs saying things such as, "Protect Mueller", "Trump is not above the law", and "Whitaker must recuse". The next attorney general could enjoy some more flexibility when it comes to enforcing federal marijuana laws.
Administration officials say that aside from the rhetoric the border really does have a problem, given that anyone who manages to get across can request asylum and subsequently often vanish while their case sits in the court system.
"The vast majority of these applications eventually turn out to be non-meritorious", a senior administration official said, asking not to be identified.
Less than 10 percent of cases result in asylum being granted, the government says.
"The government can not abdicate its responsibility towards migrants fleeing harm", the New York Immigration Coalition advocacy group said.
The busy ports of entry already had long lines and waits, forcing immigration officials to tell some migrants to come back to make their claims.
"What we are attempting to do is trying to funnel. asylum claims through the ports of entry where we are better resourced, have better capabilities and better manpower and staffing to actually handle those claims in an expeditious and efficient manner", they said.
In 2017, the US fielded more than 330,000 asylum claims, almost double the number two years earlier and surpassing Germany as highest in the world.