The incoming Mexican administration of Andres Manuel Lopez Obrador said there is no deal with the United States that would allow asylum seekers to wait in Mexico while their cases are decided after reports indicated such an agreement had been reached.

Saturday, The Washington Post reported that a deal between the Trump and Obrador administrations would begin a "Remain in Mexico" policy to replace the system – sometimes derisively called "catch and release" – of permitting immigrants to remain in the USA while their cases move through the courts, a process that can take years.

"For now, we have agreed to this policy of Remain in Mexico," Mexico’s incoming interior minister, Olga Sanchez Cordero, said, according to the Post. She described the policy as a short-term solution, while the "medium- and long-term solution is that people don’t migrate."

Later, Sanchez said, "There is no agreement of any sort between the incoming Mexican government and the U.S. government." Sanchez, who will serve as Obrador's top domestic policy official when she takes office Dec. 1, did not explain the reason for the conflicting statements.

President Donald Trump had declared in tweets, "Migrants at the Southern Border will not be allowed into the United States until their claims are individually approved in court."

"We only will allow those who come into our Country legally. Other than that our very strong policy is Catch and Detain. No 'Releasing' into the U.S.," the president tweeted Saturday. He repeated his threat to close the U.S.-Mexican border if "necessary."

"There is no way that the United States will, after decades of abuse, put up with this costly and dangerous situation anymore!" he said.

Sanchez said the immigrants pose a major headache for Mexico.

"Mexico has open arms and everything, but imagine one caravan after another after another. That would also be a problem for us," she told the Post.

Rep. Elijah Cummings, D-Md., said Sunday he does not support a "Remain in Mexico" agreement "because that's not the law."

"They should be allowed to come in, seek asylum, that's the law," Cummings told "Meet the Press" host Chuck Todd. Cummings is likely to chair the Oversight Committee when Democrats take control of the House of Representatives in January.

"I think we have a system that has worked for a long time. This president's come in, wants to change it, that's up to him. But now the Congress has got to stand up, and hopefully they will," Cummings said.

Stephanie Leutert, director of the Mexico Security Initiative at the University of Texas-Austin, said on Twitter that officials from the United States and Mexico hope a "Remain in Mexico" policy could deter Central American immigrants fleeing gang violence and poverty from seeking asylum in the USA.

"This is the most recent move by the Trump admin to deter asylum seekers from coming to the border," Leutert wrote. "The idea is to take away the ability to live & work in the US while cases are processed. The hope is that asylum seekers will not want to live in MX for months/years and won't come."

She said the policy, if enacted, would probably cut the number of asylum seekers, but she cautioned that it could persuade others to try to illegally cross the border "undetected."

About 5,000 Central American immigrants have come to Tijuana, a city of 1.6 million people just across the border from California, as part of a caravan that traveled from Honduras, then through Guatemala and Mexico. Many of the immigrants fled poverty, corruption and violence in their home countries.

Tijuana Mayor Juan Manuel Gastelum declared a humanitarian crisis Friday as Tijuana struggles to handle their arrival. Most of them are camped in a sports complex where churches and charities have been helping them with assistance from Mexican government agencies.

Contributing: The Associated Press