President Donald Trump said Friday that there is a "good chance" that U.S. and Mexican officials could strike a deal that would remove the need to impose tariffs he has threatened, shifting his tone as the two sides continued to negotiate steps to address the surge of migrants crossing the U.S. southern border.

"If we are able to make the deal with Mexico, & there is a good chance that we will, they will begin purchasing Farm & Agricultural products at very high levels, starting immediately," Trump said in a tweet. "If we are unable to make the deal, Mexico will begin paying Tariffs at the 5% level on Monday!"

He sent his tweet from Air Force One as he was returning from a trip to Europe.

Several hours earlier, a senior White House official also raised the possibility that a deal could be struck by Monday.

"There's a long way to go still, that's the bottom line," Marc Short, chief of staff to Vice President Mike Pence, told reporters at the White House, adding that the administration plans to issue a "legal notification" Friday in advance of the imposition of 5 percent tariffs Monday.

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"But I think that there is the ability, if negotiations continue to go well, that the president can turn that off at some point over the weekend," Short said.

Short said that the negotiations taking place in Washington had been "wholly insufficient" Wednesday but that the White House was "more encouraged" as of Thursday.

The Washington Post reported Thursday that U.S. and Mexican officials are discussing the outlines of a deal that would dramatically increase Mexico's immigration enforcement efforts and give the United States far more latitude to deport Central Americans seeking asylum.

The potential deal was described by a U.S. official and a Mexican official who cautioned that the accord is not final and that Trump might not accept it.

Faced with Trump's threat to impose steadily rising tariffs on goods imported from Mexico beginning Monday, Mexican officials have pledged to deploy as many as 6,000 national guard troops to the area of the country's border with Guatemala, a show of force they say will immediately reduce the number of Central Americans heading north toward the U.S. border.

The plan, a sweeping overhaul of asylum rules across the region, would require Central American migrants to seek refuge in the first country they enter after leaving their homeland, the two officials said. For Guatemalans, that would be Mexico. For migrants from Honduras and El Salvador, that would be Guatemala, whose government held talks last week with acting homeland security secretary Kevin McAleenan.

Any migrants who made it to the U.S. border generally would be deported to the appropriate third country. And any migrants who express a fear of death or torture in their home country would be subjected to a tougher screening standard by U.S. asylum officers more likely to result in rejection.

This article was written by John Wagner, a reporter for The Washington Post. The Washington Post's David J. Lynch, Nick Miroff and Kevin Sieff contributed to this report.