Mayor Bill de Blasio is already battling one governor. Now he is taking on another.

Embroiled in a long-term, internecine conflict with Gov. Andrew M. Cuomo of New York, Mr. de Blasio has embraced a second high-level feud, exchanging harsh words with Gov. Chris Christie of New Jersey over the refugee crisis in Syria.

Mr. Christie’s fierce objections to the United States policy on acceptance of refugee children have prompted scorn among liberals, and on Wednesday, Mr. de Blasio was eager to join the chorus.

“I’d like to know what Governor Christie says about this,” the mayor declared at a news conference in Manhattan, brandishing a copy of a widely circulated color photograph of a 3-year-old Syrian child who was found drowned on a beach in Turkey.

“Is this what he wants to see happen to people?” the mayor said, his voice rising, as a few supporters cheered. “Is this what he wants to see happen to children? We don’t accept that here in New York City.”