New York City Mayor Bill de Blasio’s administration has increased spending on homeless services by about 60% since he took office nearly three years ago, reaching a historic $1.6 billion this year.

At the same time, the population in city shelters is up by nearly 20%, raising questions about whether the spending has been effective in combating homelessness. Last week, more than 60,650 people, including about 23,800 children, slept in a city shelter.

Heading into a re-election year, the administration is banking on the extra funds to reverse a decadeslong rise in homelessness and is asking his toughest critics to be patient. But some longtime leaders in the social-services sector worry that the money won’t curb the uptick.

“They keep creating new programs because they still believe that they will find a magic bullet,” said Lilliam Barrios-Paoli, a former deputy mayor who oversaw homelessness until she resigned last year. “Sometimes it is easy to get caught up in the immediate crisis and to forget that you need to step back and create more permanent solutions.”

When Mr. de Blasio took office in 2014, the city shelter system had a budget of about $1 billion and a population of about 50,700.