A building owner and a City Council member are squaring off over an upcoming landmarking battle on the Upper East Side.

Most of the buildings in the City and Suburban Homes complex, which takes up an entire block between York and First avenues and 64th and 65th streets, were designated as landmarks in 1990. Two buildings that were excluded from the designation could yet be redeveloped, and neighbors fear the building’s owner, Stahl Real Estate, is moving toward constructing two soaring glass towers on the site.

The local council member, Jessica Lappin, chairwoman of the Landmarks Committee, is pushing for landmark designation of the two light-colored six-story buildings on York Avenue, opposite Rockefeller University in a sleepy corner of Manhattan. At her request, the city’s Landmarks Preservation Commission will hold a public hearing on the designation of the two buildings on Tuesday.

At a time when housing conditions in parts of the city were overcrowded, dangerous, and unhealthy, the City and Suburban Homes company was founded by prominent philanthropists who placed limits on their profits to build model tenements with abundant light, air, and running water. Completed in 1915, the buildings were part of the largest affordable housing complex ever built.

“This was a revolutionary idea, it was part of a social struggle for clean and safe affordable housing,” Ms. Lappin said yesterday, touring the outside of the buildings. “It became a national model.”

She stopped short of calling the complex attractive. “It’s charming,” she said.

For nine years, area residents and preservationists fought to landmark the full block of former tenements, along with another cluster of City and Suburban Homes farther north along York Avenue between 78th and 79th streets. At the northern complex, developer Peter Kalikow, who now heads the MTA, sought to raze the block and build an 80-story apartment building.

Eventually, both complexes were designated as landmarks, but as a “favor” to the building owners, Ms. Lappin said, the now-defunct Board of Estimate decided against designating two buildings at each complex. After neighbors sued, a court ruled that the entire 79th Street complex be landmarked. Ms. Lappin said residents could not afford a legal challenge for the 64th Street complex.

“This is an opportunity to right a wrong, to fix what was a bad backroom deal in 1990,” Ms. Lappin said.

In 1977, Stahl Real Estate purchased the complex. It contains 850 rental units, many of which are still rent-regulated. Yesterday, scaffolding going up around the building for a renovation.

A spokesman for Stahl Real Estate, Martin McLaughlin, said there is an existing agreement between the city and the owner, dating back to 1990, that the site where the two undesignated buildings sit would be reserved for development. He said the owner would consider challenging a landmark designation in court.

“The buildings are not by any stretch of the imagination landmark quality,” Mr. McLaughlin said.

He said the building owner made an offer to Ms. Lappin, asking her to hold off on pushing for landmark designation. In return, he said, Stahl Real Estate would have poured $20 million into building renovations and when it developed the site, and would have reserved about 20% of the units as affordable housing. The company, he said, was at least five years away from developing the site.

“Landmarking is not going to do anything for anybody,” Mr. McLaughlin said. “It is not going to improve the site. Down the road, it might prevent somebody from getting their views blocked.”

Ms. Lappin said the landlord’s offer was informal and that the existing buildings are already affordable. The council member said representatives of Stahl Real Estate had shown her architectural renderings for a pair of 28-story towers on the site.

“If something deserves to be landmarked, it deserves to be landmarked. There is no wheeling and dealing,” Ms. Lappin said.