A meeting this week between top U.S. and Mexican officials to discuss the ongoing migrant crisis included talks about "regularizing" illegal immigrants living in the United States, officials said on Thursday.

Secretary of State Antony Blinken and Homeland Security Secretary Alejandro Mayorkas were among the officials in the U.S. delegation to Mexico City and met with Mexican President Andres Manuel Lopez Obrador on Wednesday. The meeting came amid a historic crisis at the border, with December on track to shatter records for migrant encounters.

In the joint statement, the countries affirmed their commitments to "orderly, humane and regular migration" and stressed their efforts to tackle "root causes" of migration, disrupt human smuggling and promote private investment while also investing in "ambitious development programs" in the region.

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But the statement also said that officials discussed the "benefits" of granting some form of legal status for illegal immigrants already in the U.S., including those protected by the 2012 Deferred Action for Childhood Arrivals (DACA) — an executive order signed by President Barack Obama, which shielded some illegal immigrants who arrived in the U.S. as minors.

"The delegations also discussed the benefits of regularizing the situation of Hispanic migrants who have been undocumented for several years and the DACA beneficiaries, who are a vital part of the US economy and society," the joint statement said, adding that the delegations will meet again in January.

The Biden administration has previously called for a pathway to citizenship for millions of illegal immigrants living in the U.S. when it unveiled its sweeping immigration reform legislation in 2021. The package failed to pick up Republican support, in part due to the inclusion of the amnesty, but the administration has continued to promote it as a solution to the ongoing migrant crisis.

With a raging crisis at the southern border, attention has largely turned to increasing restrictions for asylum. The Biden administration, which has touted its efforts in tackling root causes and expanding "lawful pathways" has also said it is increasing "consequences" for illegal entry, including additional use of expedited removal and a new asylum rule restricting some claims.

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It has also requested $14 billion for border funding as part of its supplemental funding request to Congress. Republicans have demanded that the package include restrictions on the use of humanitarian parole and stricter asylum standards — something the administration has reportedly been open to, but that has met with resistance from some Democrats.

Some Senate Democrats have previously said that any policy changes at the border would have to be accompanied by a legal pathway for illegal immigrants — although such a demand would likely be a non-starter for many Republicans.

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Meanwhile, Fox News reported this week that during the four-day Christmas weekend, there were more than 35,000 migrant encounters, and since December 1, there have been over 250,000 migrant encounters at the southern border — meaning December could break the monthly record for encounters set in September (269,735).

It comes at the end of a record-setting 2023, which has seen records for daily and monthly migrant encounters broken multiple times. Another migrant caravan including thousands of migrants has also been making its way through southern Mexico.

Fox News' Bill Melugin and Griff Jenkins contributed to this report.