The City Council speaker is signaling her support for a plan to build a new hospital facility in Greenwich Village and allow Rudin Management Co. to develop hundreds of thousands of square feet of luxury housing along Seventh Avenue.

Speaker Christine Quinn, whose support for the proposal will be key if it is to make its way through the city’s land use review process, was opposed to a previous version of the plan.

“I am confident that your efforts along with the changes made by St. Vincent’s Hospital and the Rudins will lead to a new state-of-the-art hospital that the community and the entire city will be proud of,” Ms. Quinn said in a letter read to the city’s Landmark Preservation Commission by an aide at a hearing yesterday.

St. Vincent’s is seeking approval from Landmarks to sell nine of its existing buildings to Rudin for $310 million. The hospital would use the proceeds from the sale for a new facility and Rudin would then build 650,000 square feet of luxury housing along with street-level retail space, underground parking, and medical office space.

Ms. Quinn termed “vast and positive” the revisions St. Vincent’s and Rudin recently made to their plan. She also complimented the developer’s support for a new public elementary school in the district that was announced last month, to be located on Sixth Avenue between 16th and 17th streets.

Prompted by opposition from the commission, neighbors, and preservationists to the demolition of the O’Toole Building on Seventh Avenue, administrators from St. Vincent’s and the Rudin family last month presented a scaled-back version of their plan, which significantly reduced the height and width of both the proposed new hospital and the main residential tower, both of which would be situated on Seventh Avenue.

In addition to the presenting their revised plan to the commission, St. Vincent’s officials set out to prove their eligibility for a hardship exemption that would allow them to tear down the O’Toole Building, a Modernist structure where the new hospital would be built. A series of speakers testified yesterday that the hospital cannot fulfill its charitable mission while preserving the O’Toole Building.

No action was taken yesterday, but a spokeswoman said the commission would put together an advisory group composed of at least two people from the city’s Economic Development Corp. to help evaluate the plan and consult with the commission on the financial aspects of the hardship application.

Another hearing will be scheduled for July.