Washington — Facing the prospect of new tariffs imposed on all goods sent to the U.S., the Mexican government is proposing to overhaul its asylum rules and deploy thousands of troops to the country's border with Guatemala to curb the unprecedented surge of migrant families journeying to the U.S.-Mexico border.

In talks with the Trump administration — which has vowed to impose tariffs on Mexican goods starting Monday unless the Mexican government moves swiftly to reduce the number of Central American migrants trekking across its interior to reach the U.S. — representatives of President Andrés Manuel López Obrador's administration said they were willing to take bold action, a U.S. official told CBS News.

In an apparent response to a report from Bloomberg News that the White House was considering delaying the tariffs, press secretary Sarah Sanders said Thursday that the U.S. "position has not changed and we are still moving forward with tariffs at this time."

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The U.S. official said Mexican diplomats told their American counterparts during the first round of talks on Wednesday that they would be willing to station 6,000 National Guard troops along the Mexico-Guatemala border, where migrants from the so-called Northern Triangle, a region comprised of El Salvador, Honduras and Guatemala, cross to begin their journey through Mexico.

Hundreds of Central American migrants walk together on the highway, after crossing the Guatemala-Mexico border, near Ciudad Hidalgo, Mexico, Wednesday, June 5, 2019. Marco Ugarte / AP

The U.S. official also told CBS News that Mexican officials said Thursday they could come to an agreement about changing asylum policies to curtail migration patterns and accommodate proposed changes to the asylum system in the U.S.

According to a White House official, the Trump administration is considering a policy that would make migrants eligible for asylum only if the U.S. is the first country they enter from their home country. For instance, a Guatemalan migrant who travels across Mexico to reach the U.S. would not be eligible for asylum.

Further details about the ongoing negotiations — which are occurring while President Trump is traveling in Europe — were not forthcoming.

Publicly, Mexican officials stressed that no concrete deal had been brokered Thursday.

"The conversations continue advancing. We are exploring options to meet the growing number of undocumented migrants that cross Mexico. No agreement has yet been reached but we continue negotiating," Mexican Foreign Ministry spokesman Roberto Velasco Álvarez told CBS News.

On Twitter, Velasco Álvarez said U.S. officials were focused on mitigating migration, while the Mexican government was focused on "development," presumably referring to aid for the Northern Triangle to address the rampant poverty, violence and political corruption in the region.

Incensed by the large number of border apprehensions in recent months — which hit a 13-year high in May — Mr. Trump has pledged to halt all U.S. foreign aid to Central America, a longstanding pillar of American foreign policy. Aid workers stationed in the region have warned that the move is likely to backfire and fuel more migration.

Margaret Brennan, Kathryn Watson, Weijia Jiang, Arden Farhi and Fin Gomez contributed to this report.