President-elect Donald Trump on Friday defended his plans to build and fund a U.S.-Mexico border wall, saying the “dishonest media” isn’t reporting that Mexico will reimburse U.S. taxpayers for any money spent to construct it.

“The dishonest media does not report that any money spent on building the Great Wall (for sake of speed), will be paid back by Mexico later!” Mr. Trump tweeted.

Multiple reports on Friday said Mr. Trump’s team is exploring ways to construct the wall through existing legislation, which could entail asking Congress to appropriate funds to do so.

Mr. Trump repeatedly pledged during the presidential campaign that he would build a giant wall on the United States’ southern border and get Mexico to pay for it, and incoming White House counselor Kellyanne Conway said Friday he is going to follow through.

“Obviously, a centerpiece of Donald Trump’s successful campaign was ‘I’m going to build the wall and have Mexico pay for it,’ ” Ms. Conway said on “Fox & Friends.” “That hasn’t changed.”

“But Congress is examining ways … to have the wall paid for through their auspices,” she said. “The president-elect is making the point that he will have Mexico pay it back.”

“He’s going to build that wall, and Mexico is going to pay for it. That hasn’t changed,” she said.

Mexican President Enrique Peña Nieto said in August after he met with Mr. Trump that he kicked off their meeting by saying Mexico wouldn’t pay for the wall.

Mr. Trump had said the subject of payment didn’t come up in the meeting, and his team said it was an initial get-together and it would have been inappropriate to get into such details.

Mr. Trump outlined a payment plan last April in which one option would entail tightening controls on remittance payments by Mexican workers back to their families and redefining rules on wire transfers to require customers to prove they are legally in the U.S.

Mexico would object and would be told the final rule wouldn’t be imposed if they paid for the wall, according to the plan.

Other possible mechanisms in that plan included trade tariffs, canceling visas, and visa fees.

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