Councilman Ben Kallos, who chairs the Governmental Operations Committee, said in an interview that he expected DCAS to meet its target by the end of next year.

“If they’re able to turn 5,000 provisionals into civil servants in one year, that sets the tone and we should be able to get down to zero in the next three to four years,” he said, adding that capping an extension at one year would be the “responsible” option.

“Because that is the only part that can be planned for by this current administration or even by me,” said Mr. Kallos, who was elected in 2013. “We are guaranteed until the end of 2017 for our first term, and anything else should not be taken for granted.”

The Manhattan Councilman said that he requested the agency share whether there was an overlap between titles with provisional appointments and those with lists. “I will be looking to ensure—and the state should be looking to ensure—that no provisional is hired into a new title where there was an existing exam administered with somebody waiting months, if not years, to be hired into that position,” he said.

DCAS officials said they would be willing to include the number of provisionals in the Mayor’s Management Report, an annual agency report card. “If we see in September, when the MMR comes out, that those numbers aren’t there, you better believe we’ll be having an oversight hearing to see why we’re falling behind,” Mr. Kallos said.