“We were interested in working collaboratively with the Police Department,” she added. “Obviously we did not get 100 percent of what was laid out in the bills.”

In a statement released on Tuesday, Mr. de Blasio said that his administration had taken “clear steps to reduce unnecessary arrests and strengthen our officers’ relationship with the community,” noting, among other things, changes to the city’s marijuana arrest policy.

“These smart reforms will help bridge the essential relationship between police and community that is at the center of keeping our neighborhoods safe,” the mayor added.

The bills intended to alter the interactions between officers and people on the street in encounters when an officer suspected a possible crime.

One bill would have required officers to identify themselves by name, rank and command after encounters that do not result in arrest or summons; another would have required that officers, before requesting consent for a search in the absence of any legal basis, to inform the person of his or her right to refuse the search.

Under the agreement, Council officials said, officers conducting a so-called consent search of a car, a home or a person will be required to ask a question such as “Can I search your pockets?” rather than “Hey, let me search your pockets.” Afterward, they will have to confirm that the person understood his or her right to refuse. If consent is declined, the officer will have to obtain a warrant or walk away.

After such a search, the officer will be required to provide a business card. The cards, which will be printed and provided by the Police Department, will also be handed over at checkpoint car stops and upon request during informational conversations on the street that do not legally constitute a police stop, the Council officials said. Officers will be retrained in the coming months on the new procedures.