The move would effectively block most asylum protections at the border, and is part of a wider crackdown on immigration by President Donald Trump.
The new move would likely face legal challenges.
Exceptions were carved out for victims of extreme forms of trafficking, who had crossed borders against their will, and those who were unable to obtain protection elsewhere.
The changes to the regulations are meant to help fix backlogs in the immigration system by reducing the number of asylum applications, since many claims are ultimately rejected.
Critics say it blocks a key means for those in need of safety to seek refuge.
The situation at the southern border has become a key political issue in the U.S., amid a recent sharp uptick in new arrivals and overcrowding at border facilities to detain migrants crossing illegally.
“(An) alien who enters or attempts to enter the U.S. across the southern border after failing to apply for protection in a third country … is ineligible for asylum,” said the rule, which is due to come into effect on Tuesday.
Trump recently struck a deal with Mexico, after threatening the southern neighbour with tariffs on its exports, that saw the country step up security on its own borders, in an effort to reduce migration north.
Guatemalan President Jimmy Morales announced on Sunday that he was postponing his trip to the White House this week, where he had been due to discuss migration issues, with the focus again likely to be on reducing the number of people trying to migrate to the U.S.
The delay was meant to allow the judicial system in that country to deal with challenges to a proposal which would have meant Guatemala would have to process asylum claims locally, as part of a safe third country agreement.
“It was decided to reschedule the bilateral meeting until it is known what the court has decided,” a government statement said.
Trump over the weekend was accused of making racist comments towards female members of Congress, saying they should “go back” to where they came from.
While the members of Congress were not named, he was believed to be referring to four progressives, three of whom were born in the U.S.
All four are non-white U.S. citizens. They have also been outspoken critics of the detention facilities on the border.
The president doubled down on his weekend remarks on Monday morning, saying those he insulted neeeded to apologize to him, while also accusing the lawmakers of being anti-Israel.
(Edited by Emmanuel Yashim)