The International Freedom Center has until September 23 to revise its plans to accommodate the concerns of its critics, who said some of the museums’ exhibitions would be inappropriate for the World Trade Center Memorial.

If the center does not come up with a satisfactory alternative, it will be forced to follow the lead of the Drawing Center, which pulled out of the Memorial site under similar pressure from some family members of victims of the terrorist attacks of September 11, 2001.

The Drawing Center is looking to relocate to another site downtown, the board of the Lower Manhattan Development Corporation announced yesterday.

Both cultural institutions were chosen, along with two others, a year ago to compose part of the World Trade Center Memorial but were roundly criticized by families of September 11 victims, who said some of the exhibits at the two museums would be anti-American and therefore inappropriate venues for the memorial site.

The board of the development corporation, which is a partner in the International Freedom Center, said the center should work with family members and “other stakeholders” to resolve the disputes over the center’s activities.

Victims’ family members who have expressed opposition to both centers said yesterday that anything short of the Freedom Center’s moving to an alternative site would be unacceptable.

“Our position is that the International Freedom Center does not belong anywhere on the World Trade Center site,” one family member, Anthony Gardner, who represents a group called Take Back the Memorial, told The New York Sun. The group expects to continue its protest at a rally September 10 at ground zero, 24 hours before the traditional remembrance ceremonies begin.

In a statement yesterday, the International Freedom Center repeated its commitment, made in a July 6 letter to the president of the Lower Manhattan Development Corporation, Stefan Pryor, to work with the families of September 11 victims to create an exhibition center that would bring the artifacts and history of that time to the public.

“We look forward to the opportunity to further detail our plans for content and governance, and will do so in the public submission requested for September 23,” the statement read.

The development corporation’s board said in a statement yesterday that if it is not satisfied with the freedom center’s new proposal, “we will find another use or tenant – consistent with our objectives – for that space in the Snohetta building.” The reference is to the building’s architect, the Norwegian firm Snohetta.

The International Freedom Center, intended to be an exhibition and education resource, and the Drawing Center, as well as the Joyce and Signature theaters, were selected in June 2004 to occupy the building. The development corporation’s board said the building would be 30% smaller than its original design.

A museum focused on drawings and established in 1977, the SoHo-based Drawing Center said last month that it was looking to pull out of the memorial site because it did not want to face public pressure indefinitely for the kinds of exhibits it showed.

Yesterday, the development corporation’s chairman, John Whitehead, announced that the Drawing Center plans to hire a real estate adviser to generate a shortlist of alternative sites downtown, to remain a “key part of the revitalization of Lower Manhattan.” The goal would be to find an appropriate site near the memorial.