The rule requires migrants who pass through a country other than Mexico before reaching the U.S.to seek asylum there first.
In practice the changes mean that migrants from Honduras, Nicaragua and El Salvador must first claim asylum in a neighbouring country or Mexico.
He also said things were looking better for the ratification of a new free trade agreement between US, Mexico and Canada. Many of those arriving are fleeing violence or poverty.
For now, that means that "people who may have been eligible for asylum before won't be eligible for protection in the US anymore", said Jessica Bolter, an associate policy analyst with the Migration Policy Institute.
"We have a very different policy in Mexico, and we are not going to change it. Mexico's refugee and asylum policy is a tradition here", Ebrard said.
Mexico said on Thursday that it disagreed with the ruling.
Mexico 'disagrees' with Trump asylum restrictions
"I know things are getting more and more complicated in the United States", said Noel Hernández, 21, who was staying at a migrant shelter in Guatemala after leaving his home in Tegucigalpa, in Honduras, a few days ago.
That gesture has led to a decline in US apprehensions and rejections of migrants at the border, which totaled 64,000 people in August, down 22% from July and 56% from a high mark in May.
Curbing migration levels has been a key goal of Donald Trump's presidency and forms a major part of his bid for re-election in 2020.
"Our policy of refuge, of asylum is a tradition in Mexico", he said. "This rule will result in those fleeing fear and persecution to be turned away at our doorstep and will only exacerbate the humanitarian crisis in the region", House Judiciary Committee Chairman Jerrold Nadler and Zoe Lofgren, who chairs the immigration and citizenship subcommittee, said in a joint statement.
The change will affect non-Mexican migrants trying to enter through the USA southern border. The administration has said that it wants to close the gap between an initial asylum screening that most people pass and a final decision on asylum that most people do not win.
It is perhaps the biggest change to US asylum policy since it was established in 1980 and the most consequential move of President Donald Trump's crackdown on immigration, a signature issue as he heads into a re-election campaign. People from Guatemala must be denied in Mexico.
Morgan said the Trump administration is "doing everything that they can" to address what he described as the crisis on the USA border with Mexico. Tigar's ruling forbade Trump's new asylum policy in some states along the southern border.
For now, the rule will apply to those who crossed the border after July 16, who failed to apply for asylum in at least one other country before reaching the USA and who did not have a deportation proceeding before September 11, the date of the ruling, said USCIS spokesperson Jessica Collins.