JERUSALEM- The latest skirmish in the war for every inch of this coveted city focused this week on the dead. Did Israeli government bulldozers, working in the middle of the night, destroy hundreds of historic Muslim graves? Or were the removed tombstones outrageous fakes placed on parkland in a ruse?

Each side in the dispute - a fiery branch of the Islamic Movement in Israel and the right-wing Jerusalem municipality - is accusing the other of shamelessness and indecency. The area in question is in West Jerusalem, a predominantly Jewish area next to a contested site where the Simon Wiesenthal Center is planning a branch devoted to tolerance and human dignity.

"This is a despicable and, frankly, sad publicity stunt," Stephan Miller, a spokesman for the Jerusalem municipality, said of the tombstones, which he called fictitious. "It is a slap in the face of freedom of religion and the preservation of religious sites that we work day and night to ensure."

For its part, an Islamic foundation that had been fixing up and installing the headstones said that its work was entirely legal and that it believed the late-night destruction of the tombs was part of a city effort to take over the cemetery for more mundane needs.

"The municipality is simply continuing the process of confiscating the entire cemetery," said Zaki Agbaria, a civil engineer and head of the Aqsa Foundation for Islamic Waqf and Heritage. "We believe they want to change the area into a parking garage."

The foundation is associated with the northern branch of the Islamic Movement in Israel, made up of Muslim citizens of Israel.

The feud is part of a much longer, centuries-old contest for control of Jerusalem and the Holy Land as well as part of an increasingly heated dispute over a small area in West Jerusalem known as the Mamilla or Ma'man Allah cemetery.

Last February, representatives of long-established Palestinian families petitioned the United Nations for help in trying to stop Israel and the Wiesenthal Center of Los Angeles from constructing the new branch on an adjacent part of the cemetery. The project, to be known as the Center for Human Dignity - Museum of Tolerance, has been plagued by criticism since 2004, when it became clear that the 50-year-old parking lot on which it was to be built was sitting atop at least part of an old and distinguished Muslim cemetery.

The contours of the Mamilla cemetery are part of the dispute. Wiesenthal Center supporters say that there are no human remains left in the section where they plan to build, and that only part of it was ever a cemetery. They further contend that the effort to stop the project is the work of Muslim extremists seeking a foothold in West Jerusalem, and evidence of the need for such a center to spread more tolerance.

Critics of the project say it is unconscionable to build such a center on a piece of land where Muslims were once buried, even if it has not been an active cemetery for nearly a century. The museum project is going ahead after a 2008 Israeli Supreme Court decision noting that no Muslim objections had been filed when the original parking lot was built.

There remains a dispute among Muslim clerics as to whether a former graveyard can ever be built upon for other purposes.

Meanwhile, in the past couple of months, the Aqsa Foundation, with the permission of the city, has been cleaning up an adjacent area filled with graves. According to the city, the foundation moved beyond its mandated area and brought in about 300 headstones, placing them on land that had never been part of the cemetery.

The city announced plans to remove the stones, and the foundation went to court to stop the removal. The Jerusalemdistrict judge, after testimony from the Israel Antiquities Authority, agreed with the city's assessment that the stones had not been placed on top of actual graves and permitted their destruction.

That work began Monday night. On Tuesday, a Muslim sheik tried to block the bulldozing crew and got hurt. The foundation went back to court on Wednesday, saying that it must stop the destruction of graves. On Thursday, the judge called on the city, the foundation and the antiquities authority to return with further evidence to support their positions.

Mr. Miller, the city spokesman, said municipal authorities had little doubt that the area where the tombstones had been placed had not been a cemetery. On both sides of the disputed area there are, however, acknowledged gravesites.

A statement issued Thursday by the city contended that city inspectors found under the newly placed gravestones "plastic bottles, cigarette packs and irrigation piping as well as sewage manholes."