Sen. John Cornyn on Tuesday pressed incoming White House press secretary Jen Psaki on how the Biden administration will handle the migrant caravan headed to the U.S. from Central America after she announced the new president would tighten international travel limits on the pandemic. 

The exchange came after President Trump in an executive order Monday said that the U.S. would roll back travel restrictions imposed last year for air passengers who recently were in the United Kingdom, Europe and Brazil.

The restrictions would be lifted on Jan. 26, the same date as a new requirement for a negative coronavirus test for air travelers into the United States would go into effect. The reasoning behind the lifting of the earlier restrictions, according to Trump's order, was that the U.S. can expect those jurisdictions to comply with the new requirement for a negative test. 

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 But Psaki quickly said that President-elect Biden, rather than loosening travel restrictions for foreign countries, will clamp down. 

"With the pandemic worsening, and more contagious variants emerging around the world, this is not the time to be lifting restrictions on international travel," she said. "On the advice of our medical team, the Administration does not intend to lift these restrictions on 1/26. In fact, we plan to strengthen public health measures around international travel in order to further mitigate the spread of COVID-19."

Cornyn responded Tuesday: "Does that include caravans of migrants from Central America?"

One of the first major challenges the Biden administration will face is a massive migrant caravan currently making its way to the U.S. from Central America.

Friday, two groups of more than 3,000 Honduran migrants each pushed their way into Guatemala without registering as part of a larger caravan headed to the United States, the Associated Press reported. A third group entered Guatemala on Saturday. The migrants aim to reach Mexico, which is north of Guatemala, and eventually make their way to the United States border. 

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Republicans have blamed the Biden campaign's rhetoric for attracting the caravan. Biden promised a pathway for citizenship for 11 million people during his campaign and the organization Pueblos Sin Fronteras, on behalf of the caravan, called on  the incoming Biden administration to "honor its commitments."

Videos show that the caravan is traveling in tightly-packed crowds with sparse mask-wearing. 

Biden's planned nominee for secretary of Homeland Security, the agency that oversees border security, is Alejandro Mayorkas. At a Senate hearing Tuesday, Mayorkas was pressed on how he would handle the caravan by Sen. Mitt Romney, R-Utah. 

Homeland Security Secretary nominee Alejandro Mayorkas takes his seat to testify during his confirmation hearing in the Senate Homeland Security and Governmental Affairs Committee on Tuesday, Jan. 19, 2021, on Capitol Hill in Washington. (Bill Clark/Pool via AP)

"What is your intention with regards to that caravan, that is coming to our border. Is your intention to allow them just to come into our country? Will they be stopped?" Romney asked. 

"When people present themselves at our border, we apply the laws of our nation and determine whether they qualify for relief under our humanitarian laws or whether they don't," Mayorkas said. 

Romney responded that his answer appeared "uncertain." 

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"I apologize if I was uncertain. If people qualify under the law to remain in the united states, then we will apply the law accordingly. If they do not qualify to remain in the United States, then they won't," Mayorkas said. 

Romney didn't specifically push Mayorkas on how he would handle the potential coronavirus threat from the caravan. 

The Biden transition team did not respond to questions from Fox News Monday about whether it thinks Biden's campaign rhetoric caused the caravan and whether Biden plans to allow those in the caravan into the U.S. It also didn't say whether those entering the U.S. from the caravan will be subject to the same coronavirus protocols as air travelers.