Two nights after Donald J. Trump won the presidential election, Archbishop José H. Gomez convened an interfaith prayer service at the Roman Catholic cathedral in Los Angeles and gave an emotional homily vowing not to abandon children and parents who are living in fear that Mr. Trump will follow through on his promise to deport millions of immigrants.

“This should not be happening in America,” said Archbishop Gomez, who is himself an immigrant from Mexico and a naturalized United States citizen. “We are not this kind of people. We are better than this.”

Five days later, on Tuesday, Archbishop Gomez was elected by his brother bishops at their meeting in Baltimore to be vice president of the United States Conference of Catholic Bishops. With nine candidates in the running — including some prominent prelates — it was the day’s most closely watched vote, especially since the vice president is traditionally elevated to president in three years. Keeping to custom, the bishops voted to bump up Cardinal Daniel N. DiNardo, archbishop of Galveston-Houston, to president.

The choice of Archbishop Gomez was only one sign that Catholic bishops are preparing to defend immigrants and refugees against a newly elected president who has threatened deportations and who critics say has uncorked an ugly backlash against immigrants and minorities. They opened their meeting by endorsing a strongly worded letter to Mr. Trump that extended congratulations but also put him on notice that the church was committed to resettling refugees and keeping immigrant families intact.