Mayor Bill de Blasio of New York, in an hourlong session with President-elect Donald J. Trump — a man Mr. de Blasio once called uniquely unqualified for the presidency — cautioned Mr. Trump against large-scale deportations and what the mayor characterized as divisive language and policies that have heightened fears among New Yorkers.

“The ball’s in his court,” Mr. de Blasio said outside Trump Tower in Manhattan, at a news conference Wednesday after the meeting. “People in the city and all over the country are looking to see what he’s going to do.”

Citing a rise of anti-Semitism in the city, he added, “Part of why I think it’s so important to remind the president-elect and his team that there are deep fears and concerns out there is because the wrong messages can encourage hateful acts. So, I certainly made clear that I think sending a message of unity is crucial.”

Signaling a conservative Supreme Court justice?

One of the items on the president-elect’s to-do list is to find someone to fill the Supreme Court seat vacated by the death of Antonin Scalia.

To that end, Mr. Trump met on Wednesday with Leonard Leo, the executive vice president of the Federalist Society, a group that advocates a conservative and libertarian approach to the law. Mr. Leo said the president-elect seemed committed to picking someone who cares “very deeply about the rule of law and about the preservation of our Constitution.”

“He’s looking for someone who is independent, courageous, smart, very high quality,” Mr. Leo told reporters, adding that Mr. Trump remained committed to choosing one of the 21 court prospects he circulated during the campaign.