As the wrangling begins over how to pay for the Metropolitan Transportation Authority’s ambitious new subway rescue plan, officials offered news on Wednesday that was unlikely to make riders happy: Fares will probably rise again.

The authority’s chief financial officer, Robert E. Foran, said officials planned to raise fares for subway and bus riders in 2019 and 2021. The last fare and toll increase occurred in March, when the price of a weekly MetroCard rose by $1 to $32.

At the authority’s monthly board meeting in Lower Manhattan, Mr. Foran said the agency needed to continue to raise fares by about 4 percent every other year as part of its long-term financial plans. But some board members bristled at the biennial ritual, especially as service deteriorated.

“I think it is time now for us and our partners at the state to review or re-evaluate the every-other-year fare and toll discussion,” said Mitchell Pally, a longtime board member. “I don’t think that’s sustainable.”