"In effect, the rule forbids nearly all Central Americans [.] to apply for asylum in the United States if they enter or seek to enter through the southern border, unless they were first denied asylum in Mexico or another third country", she wrote.
The Supreme Court's decision on Wednesday permits the new rule to go forward as legal action against it continues to go through the court system.
"Once again, the Executive Branch has issued a rule that seeks to upend longstanding practices regarding refugees who seek shelter from persecution", Sotomayor wrote.
He also said things were looking better for the ratification of a new free trade agreement between US, Mexico and Canada.
"(This decision represents a) massive reversal of American leadership to protect the most vulnerable people fleeing extreme violence and persecution from around the world", he said in a statement.
A record number of Central American families have sought asylum in the United States during the past year, and most have been released to await court hearings, thwarting Trump's efforts to curb a new wave of migrants.
The policy affects people who travel to the USA through Mexico from Central America.
His conciliatory approach contrasts sharply with a line taken earlier this year by Trump, who tied immigration to economic policy by threatening crippling tariffs on all Mexican imports.
"But of course we don't know how many of those are formal asylum seekers", he added.
Mexico 'disagrees' with Trump asylum restrictions
Within hours of the ruling, senior administration figures said they would move instantly to implement the changes.
"Part of why Sotomayor and Ginsburg voted to dissent is that on the merits, the district court might have got this one right", Stephen Vladeck, a law professor at the University of Texas at Austin, told me. "WIN for the Border on Asylum!"
Curbing migration to the United States has been a key goal of his presidency and forms a major part of his bid for re-election in 2020.
The change will affect non-Mexican migrants trying to enter through the USA southern border.
On Thursday, Lopez Obrador said that he spoke by phone with President Donald Trump a day prior, noting the United States president recognised Mexico's efforts and relations between the two countries were very good.
The Trump administration says the policy is created to address deficiencies in an immigration system in which immigrants often pass initial asylum screening but fail to win final approval.
"This is the latest step in terms of Trump's policies to push Mexico to become a safe third country, and to make a big chunk of the migration flow stay in Mexico permanently and deter them from traveling north", said Raúl Benítez, a professor of worldwide relations at the National Autonomous University of Mexico.
Under the new rules, migrants would be barred from seeking asylum in the U.S. if they have traveled through a third "safe country" en route to the American border, unless they also applied for asylum in that country.
This is the second time in 2019 that the Supreme Court has ruled in favor of the Trump administration on a controversial immigration issue. "We want them to get help and seek asylum in the first country they get to".
US wants to make 'meaningful progress' in China trade talks
The Tariff Commission said that additional lists of waivers will be announced in the future, reported Chinese news agency Xinhua . He said the delay had been requested by China, and also follows a move by Beijing to scrap some United States tariffs.