On Wednesday, Mr. de Blasio told reporters that he would announce the details “in a few days” and that New Yorkers would understand if it “takes a few extra days.” Mr. de Blasio said the city was considering how it could include pay-per-ride MetroCards, which are often favored by New Yorkers who are living paycheck to paycheck.

The city agreed to pay $106 million for the first six months of the program. Under the agreement, it would apply to New Yorkers below the federal poverty line — a household income of about $25,000 for a family of four.

[Gov. Andrew M. Cuomo canceled the full shutdown of the L train between Brooklyn and Manhattan.]

For transit advocates who aggressively pushed Mr. de Blasio to support the idea, his failure to start the program on time or to publicize it has been frustrating.

“To see people not taking this as incredibly seriously as they should be, it is disappointing to say the least,” said David R. Jones, president of the Community Service Society of New York, an antipoverty nonprofit. “This is not just any ordinary mayor, this is a mayor who guaranteed he’d make this the most equitable city in the nation.”

Mr. de Blasio has struggled at times to prove he is skilled at managing a sprawling city government. And he has recently received criticism for spending less time at City Hall and for his hands-off management style.

Mr. Johnson, who has been an enthusiastic supporter of Fair Fares, has not yet joined in the chorus of criticism over the start of the program. His office said in a statement on Wednesday that Mr. Johnson was “working to make sure that Fair Fares is a success.”

“The Council has always believed that this program is for all New Yorkers living at or below the federal poverty line, and is committed to making sure that vision becomes a reality,” said Breeana Mulligan, a Council spokeswoman.