On city buses, which carry more than two million people each day, Mr. Byford suggested sending police officers onboard to enforce the rules.

“The big thing we’re missing is we need cops on buses,” Mr. Byford said at a recent transit board meeting.

But his comments drew an immediate backlash from critics, who said the move would “exacerbate the over-policing of communities of color.” Fare evasion arrests have disproportionally targeted black and Hispanic men.

Mr. Byford later clarified that he did not want to see more arrests, but that the presence of officers would discourage riders from breaking the rules. “I’d love it if no one actually got caught,” Mr. Byford said.

The authority’s new chairman, Patrick J. Foye, said he also did not want to focus on arrests and wanted to find other solutions. He said the rollout of a new fare payment system using smartphones, which starts in May, would make it easier to check if someone paid the fare.

“I do not believe in criminalizing fare evasion,” Mr. Foye said at a recent State Senate hearing.

Riders who fail to pay the fare can receive a civil summons with a $100 fine. They can also be arrested on a “theft of services” charge, a misdemeanor carrying up to a year in jail, if they have a history of similar arrests or lack valid identification.

Transit advocates say the prevalence of fare evasion reflects how many New Yorkers struggle to pay for the basics, like subway and bus fares. After intense lobbying by advocates, Mayor Bill de Blasio introduced a discount program this year that provides half-price MetroCards for poor New Yorkers. But it included far fewer people than expected.