US President Donald Trump has tweeted that migrants at the US-Mexico border would stay in Mexico until their asylum claims were individually approved in US courts, but Mexico's incoming government has denied striking any deal.

Mexico's incoming interior minister said there was "no agreement of any type between the future government of Mexico and the United States.

Olga Sanchez Cordero, also the top domestic policy official for president-elect Andres Manuel Lopez Obrador who takes office on 1 December, told Reuters that the incoming government was in talks with the United States but emphasised that they could not make any agreement since they were not yet in government.

Sanchez ruled out that Mexico would be declared a safe third country for asylum claimants, following a Washington Post report of a deal with the Trump administration known as "Remain in Mexico," which quoted her calling it a "short-term solution."

The plan, according to the newspaper, foresees migrants staying in Mexico while their asylum claims in the United States are being processed, potentially ending a system Trump decries as "catch and release" that has until now often allowed those seeking refuge to wait on safer US soil.

"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 US," Trump said in a tweet late yesterday.

"All will stay in Mexico," Trump added in second tweet, that also threatened to close the US southern border if necessary.

Jenna Gilbert, managing attorney for the Los Angeles office of Human Rights First, a legal rights organisation, said Mr Trump's plan is "outright illegal, and I'm sure the administration will once more see itself in court."

Trump has been seeking to block thousands of Central Americans traveling in caravans from entering the United States, and has ordered that immigrants who enter the country illegally from Mexico are ineligible for asylum.

That order has been temporarily suspended by a US judge.