Airbnb said on Wednesday that it was willing to crack down on individuals in New York City who rent out multiple homes, bowing to pressure from politicians and tenants’ rights groups who say the company has worsened affordable housing issues in the city.

The company also said, in a proposal to city officials, that it was willing to create a registry of hosts to make it easier for the state to enforce housing rules and that it would create a hotline for neighbors’ complaints. It would bar hosts who violated local regulations three times, and it said it had already taken 3,000 commercial operators off its service.

Airbnb has had an unusually contentious relationship with New York. The company’s attempts to court local support have alienated a broad array of powerful interest groups, including hotel unions, landlord and tenant groups, affordable housing advocates, Republicans and Democrats.

In June, state lawmakers voted to impose steep fines on anyone who rents out a whole apartment on Airbnb for fewer than 30 days. Such short-term rentals have been illegal since 2010. That bill was delivered to Gov. Andrew Cuomo on Tuesday. Mr. Cuomo now has 10 days to veto it or let it become law.