Updated at 7:22 p.m. ET

President Trump tweeted that talks with Mexican officials would continue Thursday, raising hopes they may be able to reach an agreement to avert potentially crippling tariffs on Mexican imports.

The possibility of a deal comes amid great pressure from the Mexican government and top Republican leaders who warned of potentially disastrous consequences.

Last week, Trump said that he would impose a 5% tariff starting June 10 on all imported goods from Mexico that would "gradually increase" until the flow of undocumented immigrants across the border stopped.

With Trump overseas, Pence hosted the White House meeting Wednesday with Secretary of State Mike Pompeo, acting Department of Homeland Security Secretary Kevin McAleenan, Mexican Foreign Minister Marcelo Ebrard and other top U.S. and Mexican officials to see whether they could avert a potential economic crisis.

Following the meeting, Pence tweeted that he, Pompeo and McAleenan made clear that "Mexico must do more" to address the migration crisis.

Trump added that talks would continue another day, but with the clear understanding that if an agreement is not reached, the 5% tariffs will be imposed on Monday.

"Progress is being made, but not nearly enough!" he tweeted.

Ebrard described a cordial meeting where each side clearly articulated and defended its point of view. He said the two sides will spend several hours discussing several topics to see whether they can get even closer in order to reach an agreement.

Top GOP lawmakers break with Trump

In a rare public divide, many top Republicans tried to persuade Trump not to carry out this threat, charging that the tariffs are nothing but additional taxes that would hurt the U.S. economy and do little to resolve the influx of undocumented immigrants.

"There is not much support in my conference for tariffs, that's for sure," Senate Majority Leader Mitch McConnell, R-Ky., told reporters Tuesday.

But the Republican front is not so united, with key members like Sen. Marco Rubio, R-Fla., speaking out on behalf of Trump and the tariffs.

Rubio tweeted Wednesday reports of Mexican officials failing to stop hundreds of Central Americans crossing the border with Guatemala.

"I don't generally like tariffs either," Rubio tweeted. "But what alternative do my GOP colleagues have to get #Mexico to secure its southern border, use the Isthmus of Tehuantepec to screen northbound rail cars & vehicles & act on intel we provide on human traffickers?"

"Full-blown emergency"

Giving the Trump administration greater ammunition to call for stronger action, U.S. Customs and Border Protection announced Wednesday that more than 144,000 migrants were taken into custody after crossing the Southern border in May, the third consecutive month that immigration authorities have encountered more than 100,000 migrants at that border.

"We are in a full-blown emergency," said acting CBP Commissioner John Sanders.

Trump's top trade adviser, Peter Navarro, said Wednesday morning on CNN that the tariffs "may not have to go into effect" if Mexico agrees to several steps to stop the flow of undocumented immigration.

They include enforcing its own immigration laws, securing its southern border with Guatemala and committing to taking "all the asylum-seekers."

On Wednesday, a group of seven former U.S. ambassadors to Mexico representing both Republican and Democratic administrations called on Trump to abandon the threats and "de-link trade and immigration."

Carlos Pascual, who served as a U.S. ambassador to Mexico during the Obama administration, warned higher tariffs won't solve the immigration problem and will ultimately lead to higher costs for American consumers as well as lost jobs because of the damage done to U.S.-Mexico supply chains.

"The United States and Mexico have to work together in order to resolve a problem that fundamentally addresses the interest of both countries," Pascual said. "It can't be resolved unilaterally."

Mexico's case

Mexican President Andrés Manuel López Obrador spoke optimistically this week that tariffs could be avoided, as did Ebrard, who told reporters Tuesday he saw an 80% chance that Trump would not impose the penalties.

After Wednesday's meeting, Ebrard did not back off from his optimism on reaching an agreement. He said the conversation focused on migration and not the specific tariffs. He said the Mexican government is seeking more long-term solutions to address the crisis in Central America but officials understand that the current migratory situation can't continue, citing the rising numbers of migrants crossing through the United States.

"The flows are increasing excessively," Ebrard said in Spanish. "We can't allow this to continue as it is, and tomorrow we're going to work various hours to explore [how] we can get closer on various positions."

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