The mayor said during a news conference on Wednesday that the modest number reflected a “sober” analysis of the challenge, a calculation that he said took place before each of his administration’s promises.

“I don’t think it’s a shift to pragmatism,” Mr. de Blasio said. “I think we’ve been very pragmatic on all of our numerical goals.”

But the homelessness plan reflected an evolution of the mayor’s thinking about the crisis, which even as late as July 2015 he was reluctant to acknowledge was occurring.

“Homelessness is not going up, thank God,” Mr. de Blasio said then at a news conference, disputing the idea that the problem had grown more visible as “factually wrong.” The mayor added that he then felt it was “largely a mental health challenge.”

By Tuesday, it was clear that the mayor had moved beyond that thinking, presenting a 128-page plan that underscored the complex effects of housing affordability, stagnant wages, economic opportunities, city outreach efforts and government subsidies on the number of New Yorkers who fall into homelessness. (The plan followed another, released in April 2016, that promised no fixed numerical goal for reducing the city’s shelter population.)

Rather than an evolution in governing style, though, some observers said the mayor’s plan could be read as a purely political gambit aimed at neutralizing a potential liability as he faces re-election.

“In an election year, there is no practical; just political,” said Evan Thies, a Democratic political consultant. “In this case, though, the practical decision and the political one happen to be the same thing.”