WASHINGTON (AP) — U.S. and Mexican officials headed into a second day of talks Thursday, working to avert import tariffs that President Donald Trump in threatening to impose as he tries to strong-arm Mexico into stemming the flood of Central American migrants at America's southern border.

Both sides claimed headway in lengthy talks Wednesday, but Trump said a "lot of progress" must still be made to halt the 5% tax on all Mexican goods that he has threatened to impose Monday as part of an escalating tariff regime opposed by many in his own Republican Party.

Underscoring the scope of the border problem, the Department of Homeland Security announced Wednesday that U.S. Border Patrol apprehensions of migrants illegally crossing the border hit the highest level in more than a decade in May: 132,887 apprehensions, including a record 84,542 adults and children traveling together and 11,507 children traveling alone.

Trump, who is currently traveling in Europe, tweeted from Ireland that the Washington talks would continue "with the understanding that, if no agreement is reached, Tariffs at the 5% level will begin on Monday, with monthly increases as per schedule."

Staff level talks with Mexican officials were resuming at the White House and State Department, though it remained unclear what kind of deal could be struck with Trump out of the country. U.S. officials were preparing for the tariff to kick in Monday barring major Mexican action.

"We'll see what happens," Trump told reporters in Ireland before leaving for France to attend a D-Day ceremony. "But something pretty dramatic could happen. We've told Mexico the tariffs go on. And I mean it, too. And I'm very happy with it."

Vice President Mike Pence, who led the discussions Wednesday with Secretary of State Mike Pompeo and other U.S. officials, echoed Trump, saying: "We made clear to them that President Trump is going to continue to stand firm until we bring this crisis of illegal immigration on our southern border to an end."

White House officials had downplayed expectations ahead of Wednesday's meeting, saying the U.S. was willing to listen to Mexico's ideas for meeting Trump's demands but did not expect a deal to emerge.

And during the discussion in the Roosevelt Room, the gulf between the countries was clear as Mexico offered small concessions and the U.S. demanded major action. A senior administration official briefed on the talks said the U.S. once again pressed Mexico to enter into a "safe third country agreement" that would make it difficult for those who enter Mexico from other countries to claim asylum in the U.S. Mexico has long resisted that request.

The person spoke on condition of anonymity to describe the closed-door meeting.

Administration officials have also said Mexico can prevent the tariffs by securing its southern border with Guatemala and cracking down on criminal smuggling organizations. But the U.S. has not proposed any concrete metrics to assess whether Mexico is complying, and it is unclear whether even those steps would be enough to satisfy Trump on illegal immigration, a signature issue of his presidency and one that he sees as crucial to his 2020 re-election campaign.

Mexican Foreign Secretary Marcelo Ebrard described the talks as "cordial" and told reporters at the Mexican Embassy that both sides had acknowledged "the current situation cannot keep going" because of the surge in migrant flows.

The tariffs carry enormous economic implications for both countries, and politically they underscore a major ideological split between Trump and his party. Trump has increasingly relied on tariffs as a bludgeon to try to force other nations to bend to his will, dismissing warnings, including from fellow Republicans, about the likely impacts on American manufacturers and consumers.

Republicans in Congress have been threatening their own confrontation with Trump, warning the White House that they are ready to stand up to the president to try to block his tariffs, which they worry would spike costs to U.S. consumers, harm the economy and imperil a major pending U.S.-Mexico-Canada trade deal .

The Republican president slammed his critics in Congress but focused on Democrats, accusing them of not wanting to fix U.S. immigration laws. A "lot of people, senators included — they have no idea what they're talking about when it comes to tariffs," Trump said. "They have no — absolutely no idea."

Trump himself routinely mischaracterizes who pays for tariffs, wrongly insisting it is the countries he levies them on rather than U.S. importers and often American consumers who face higher prices when costs are passed along.

Without a deal, the first tariffs — 5% taxes on imports from Mexico, eventually increasing to 25% — are to go into effect next Monday. Trump has been seething for months about the spike in migrant crossings and has proposed increasingly drastic action, including completely sealing the U.S.-Mexico border.

Most of the migrants trying to enter the U.S. are from Guatemala, Honduras and El Salvador, countries wracked by gangs, violence and poverty.

Republican lawmakers who have been in talks with officials from both countries, expressed optimism Wednesday that a deal could be reached.

Sen. Ron Johnson of Wisconsin said Wednesday he called the Mexican ambassador to underscore that Trump was serious about the tariffs and that it's unclear if Congress would be able to muster enough votes to block them from a presidential veto.

The stakes are clear: The 25-year-old North American Free Trade Agreement made trade with Mexico largely duty free. As a result, manufacturers have built up complicated supply chains that straddle the border. Americans bought $378 billion worth of Mexican imports last year, led by cars and auto parts. Mexico is America's No. 2 export market behind Canada.

The back-and-forth could also imperil the NAFTA revamp, which Trump pressured Mexico and Canada to agree to last year . The U.S.-Mexico-Canada Agreement has been signed by all three countries but must be approved by their legislatures.

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Associated Press writers Zeke Miller, Paul Wiseman, Lisa Mascaro, Darlene Superville and Padmananda Rama contributed to this report.