On the heels of Donald Trump’s acceptance of the Republican presidential nomination, President Obama will give his Mexican counterpart a megaphone Friday to criticize Mr. Trump’s plans to build a border wall and restrict immigration.

Mr. Obama will host Mexican President Enrique Pena Nieto at the White House for a discussion of trade, border security and efforts to combat drug trafficking.

After their Oval Office meeting, the two leaders will hold a joint press conference, where Mr. Trump is likely to be the elephant in the room. The Republican presidential nominee has built his candidacy partly on anti-immigration rhetoric and his promise to make Mexico pay for a wall along its border with the U.S.

White House press secretary Josh Earnest portrayed the timing of the presidents’ meeting as innocent.

“This is not an unusual occurrence,” he told reporters. “I don’t know exactly how President Pena Nieto plans to address the question about the Republican nominee, but presumably one of you will ask him and give him the opportunity to do so.”

Mr. Obama and Mr. Pena Nieto met last month at a summit in Canada, and Mr. Trump featured prominently in press questions there. At the time, Mr. Pena Nieto criticized the Republican candidate indirectly, saying “isolationism cannot bring prosperity to a society.”

On his website this week, Mr. Trump elaborated on his plans for a wall with Mexico, saying it would cost $5 billion to $10 billion and use the leverage of blocking remittance payments from Mexicans living in the U.S. to their families in Mexico. His plan would include a regulation stating that “no alien may wire money outside of the United States unless the alien first provides a document establishing his lawful presence in the United States.”

“It’s an easy decision for Mexico: make a one-time payment of $5-10 billion to ensure that $24 billion continues to flow into their country year after year,” Mr. Trump said.

If Mexico doesn’t agree, he said, he would start tougher enforcement of trade rules and cancel travel visas for Mexican nationals.

“Mexico has taken advantage of us in another way as well: gangs, drug traffickers and cartels have freely exploited our open borders and committed vast numbers of crimes inside the United States,” he said. “The United States has borne the extraordinary daily cost of this criminal activity, including the cost of trials and incarcerations. Not to mention the even greater human cost. We have the moral high ground here, and all the leverage.”

Mr. Obama and Mr. Pena Nieto will also discuss deeper cooperation on border security, Mr. Earnest said.

“There’s never been a greater commitment to border security,” Mr. Obama said. “It’s reflected in the numbers that we see of individuals who are apprehended attempting to cross the border. Part of that strategy includes effective coordination with the Mexican government.”

Also on the agenda is the Trans-Pacific Partnership, a free trade deal including both nations and 10 other countries around the Pacific Rim.

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