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Julián Castro, the federal housing secretary, whom Hillary Clinton has mentioned as a potential running mate, said Monday that if Republicans “recklessly” abandoned the Affordable Care Act without replacing it with “something thoughtful,” Latinos would “suffer tremendously.”

Mr. Castro spoke at an event hosted by the Latino Network of The New York Times, where he discussed the role of Latino voters in the coming election.

Health care, Mr. Castro said, would be a major issue.

“Millions of Latinos have benefited from the Affordable Care Act,” he said of President Obama’s signature achievement, which most Republican candidates have pledged to reverse. “That has been the biggest beneficiary community from Affordable Health Care,” Mr. Castro said, warning Republicans against repeal or efforts to “rearrange so much that it doesn’t work.”

Mr. Castro also talked about Senator Marco Rubio of Florida and Senator Ted Cruz of Texas, saying that each would have to reassure Latino voters that they would have their interests at heart. But, he added, political campaigns are about more than race.

“Rubio and Cruz, I believe that they’re running the race they believe they have to run in order to win the Republican primary,” Mr. Castro said, adding that President Obama’s two successful White House campaigns depended on more than just African-American voters.

“So, in that sense, I don’t begrudge Senator Rubio or Senator Cruz for not always reminding people that they’re Hispanic,” Mr. Castro said. “You need to represent the whole country.”

As for his own potential role in a Clinton campaign, Mr. Castro said he had not yet been vetted or contacted by Mrs. Clinton about being her running mate, and he did not comment on whether he would entertain such an invitation.