If the courts approve the municipality's request, it will be one of the largest demolitions since Israel captured traditionally Arab East Jerusalem in the 1967 Middle East war, and would cause an uproar among Palestinians who claim that part of the city as a future capital.
Aljazeera has quoted Palestinian Negotiations Minister Saeb Erekat as calling for the international community and the Quartet's immediate intervention to prevent the Israeli authorities from carrying out the demolitions.
The 88 homes are located in east Jerusalem's Arab neighbourhood of Silwan, just outside the walled Old City, an area steeped in biblical history.
The municipality wants to enlarge a small archaeological site beside the homes and turn the area into a national park, the Haaretz newspaper quoted Uri Shetrit, the Jerusalem city engineer, as saying.
The park would connect several Jewish settlement enclaves in Silwan to the nearby City of David - an area of excavations dating to the biblical King David.
In November, Shetrit wrote a letter to the director of the city's construction department, describing the "national and international importance" of 5000-year-old-archaeological shards discovered in the area.
The 88 homes are located in east
Jerusalem's Silwan locality
In light of the discoveries, "I order the removal of all illegal construction in the King's Valley," Shetrit wrote in the letter, referring to the area by its Jewish name.
Shetrit, who was not available for comment on Tuesday, wrote that the law permits the demolitions because the homes were built on land designated in 1977 as a "green area" where no construction was allowed.
In February, Silwan resident Mohammed Bardan, 43, received an order to appear in court. The order states the municipality's intention to demolish his home because it is on land designated as "open public territory".
Bardan said his home was built by his father in 1961 - six years before Israel captured the area. Pulling out reams of documents - including a tattered, yellowed Ottoman-era deed to the property - Bardan points to the road in front of his house, recalling the day Israeli soldiers first walked down the block in 1967.
"I was born here, my life is here. It may not be the fanciest place, it's actually the smelliest place in the city, but I want to stay in my house," Bardan said.
Sami Arshid, Bardan's attorney, said he represents five residents who own the oldest homes in the area, some built more than 40 years ago. At least another 15 people in the neighbourhood have also received orders to appear in court, Arshid said.
Jerusalem is at the heart of the
A decision is expected in Bardan's case on 3 July, and will likely set the precedent for the rest.
Bardan retired from the Jerusalem municipality's sanitation department 18 months ago.
He says his payback for 20 years of loyal service is the demolition - which according to court documents he would have to pay for.
The municipality acknowledged in court that it is barred from demolishing homes built without permits if they are more than seven years old, according to court documents.
However, the homeowners could be barred from residing in the buildings.
"The building offence runs out, but there's no statute of limitations on using the illegal house, so we can bar residents from entering their homes even if we can't destroy them," Haaretz quoted Shetrit as saying.
He said he hoped it would be easier to demolish an abandoned house later on.
Palestinians and Israeli human-rights groups have said Israel is using zoning and other administrative tools to keep a lid on Palestinian population growth in Jerusalem.
Palestinians have complained that it is often difficult for them to obtain building permits in East Jerusalem, and that they have no choice but to build illegally.
Israelis and Palestinians both claim Jerusalem as their capital, and the city's fate is at the heart of the Israeli-Palestinian conflict.
Danny Seidemann, an Israeli human-rights activist, said that the demolition would be one of the largest since 1967 in a single area of Jerusalem.
"We are getting rid of 21st-century human beings to make room for 3000-year-old memories"
Israeli human-rights activist
He said that about 160 homes were destroyed in 2004, but that they were spread across all Arab neighbourhoods of Jerusalem.
In Silwan, "the intention of the municipality is very clear, and that is to rid the area of its Palestinian residents," said Seidemann, who heads Ir Amim, a Jerusalem settlement-watchdog group.
"We are getting rid of 21st century human beings to make room for 3000-year-old memories," Seidemann said, adding that the municipality suffers from "moral autism".
"I don't fault the authorities for seeing the archaeological artifacts as of enormous importance to the Jewish people, but I do fault them for being blind to the human reality of this Palestinian neighbourhood," Seidemann said.