President Trump on Wednesday teased what he called “phase two” of his border deal with Mexico, saying much tougher measures are waiting in the wings if the new national police and immigration repatriation measures agreed to last week don’t stop the flow of migrants.

Journalists got a partial sneak peak at what phase two might look like a day earlier when Mr. Trump waved a paper at reporters he said contained the details of the secret deal he struck with Mexico.

A photographer’s shot showed the text of signed agreement, which seemed to commit Mexico to more forceful measures should its public commitments last week fall short of stemming the flow of people.

That undercut the mocking claims of some media pundits and critics who’d speculated the paper was blank.

“You were able to read it through the sunlight,” Mr. Trump told reporters, a bit sheepishly, at a Wednesday press conference. “That was not anticipated.”

Mexico has denied there is any secret deal beyond what was publicly announced last week: a commitment to disrupt smugglers, deployment of 6,000 national police to the border region, and agreement to expand a program to hold onto Central American asylum seekers while their cases proceed in the U.S.

The folded one-page paper Mr. Trump waved Tuesday was caught on photographs illuminated by sunlight. Portions of the text were legible.

“The Government of Mexico will take all necessary steps under domestic law to bring the agreement into force with a view to ensuring that the agreement will enter into force within 45 days,” it reads in part.

The president marveled to reporters on Wednesday, “It was closed, and you were able to read it through the sunlight. I did not do that on purpose.”

After months of blasting Mexico over the border, Mr. Trump in recent days has been exceptionally complimentary to America’s southern neighbor, saying he expects big things from the new deal.

“I think Mexico really wants to produce. If Mexico does a great job, then you’re not going to have very many people coming up,” he said.

But he warned: “If they don’t, then we have phase two. Phase two is very tough. But I think they’re going to do a good job.”

Mr. Trump contrasted Mexico’s new spirit of cooperation with the antagonism his immigration plans have earned from political opponents.

“Right now Mexico is helping us much more on immigration than the Democrats in the U.S.,” the president said.

He has asked Congress for an emergency infusion of $4.5 billion to provide better care for the children and families surging at the border. He’s also asked Congress to alter the policies that serve as an incentive to the new surge, such as a 2015 court ruling that requires illegal immigrant families to be released within 20 days of their capture.

Democrats are torn over the money. Key senators said this week they will accept most of the president’s request, which funds better conditions for immigrant children and families who are living in the U.S. illegally, but they won’t agree to more money to hold single adult immigrants caught trying to cross the border illegally, or criminal migrants caught in the interior.

They also want to attach conditions to the money to expand inspections of detention facilities, and to prohibit information sharing on sponsors who come forward to take immigrant children living in the U.S. illegally.

Often those sponsors are, themselves, immigrants who are in the U.S. illegally and sometimes live in households with deportation targets.

The Trump administration says if the government becomes aware of those targets, they should be able to act. Democrats say the households should be protected if they are willing to sponsor an immigrant child who is living in the U.S. illegally.

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