"The United States should take into consideration the Israeli measures and ask Israel to stop," Abbas told reporters in Amman after talks with Jordan's King Abdullah II. "We reject such actions, which hinder any political progress."
Washington also warned that the project "undermines trust" and could hinder the indirect negotiations between Israel and the Palestinians that started in May.
"This can't stand," Palestinian chief negotiator Saeb Erakat told AFP in Amman.
"I have conveyed a message from president Mahmud Abbas to the American administration this morning, urging their direct intervention to revoke this Israeli order," he said.
Even Israeli Defence Minister Ehud Barak was critical of the move, which could prove embarrassing for hawkish Prime Minister Benjamin Netanyahu coming two weeks before he is due to hold talks with US President Barak Obama.
Barak, who was in Washington for talks with US officials, said the announcement lacked "common sense" although his remarks focused on the timing rather than the substance of the decision.
"Jerusalem municipality and the (planning and building) committee are not demonstrating any common sense or any sense of timing -- and it is not the first time," Barak said a statement released by his office.
His remarks alluded to an earlier decision in March, when Jerusalem's city council announced, during a visit by US Vice President Joe Biden, plans to build 1,600 Jewish homes in the city's eastern sector.
The announcement provoked a crisis in relations between Israel and its biggest ally.
Around the same time, Netanyahu asked Jerusalem Mayor Nir Barkat to delay the so-called Gan Hamelech (King's Garden) project to avoid further straining ties with Washington.
But the plan was put before the city's planning and building committee on Monday, which approved Gan Hamelech, the Hebrew name for an area outside the Old City known as Al-Bustan to its mostly Arab residents.
Under the plan, 22 homes would be razed, while another 66 would be legalised. The 88 homes all had been slated for demolition because they were built without Israeli permits.
The Israeli group Ir Amim, which supports the peaceful sharing of Jerusalem and tracks developments in the city, said the project still required the approval of the district committee and would be open to public discussion.
"It still has a long way to go. I don't think the district committee will be in such a hurry to approve it because this is very sensitive politically," spokeswoman Orly Noy said.
"Any unilateral Israeli construction, especially in the Holy Basin... which is so close to the Temple Mount, has political significance," she said, using the Jewish name for the site known to Muslims as Haram al-Sharif (the Noble Sanctuary) and revered by both religions.
Many Palestinians in east Jerusalem risk having their homes razed because they were built or expanded without the necessary permits, which are nearly impossible to obtain.
Al-Bustan is part of the so-called Holy Basin, just outside the walls of Jerusalem's famed Old City, and is believed to be the site of ancient Jerusalem during the time of the biblical kings David and Solomon.
It is now a crowded Arab neighbourhood in a part of the city occupied by Israel in the 1967 Middle East war and annexed in a move not recognised internationally.
Israel considers the whole of Jerusalem as its "eternal and indivisible" capital, while the Palestinians see east Jerusalem as the capital of their promised state.
The UN envoy to the peace process Robert Serry called the municipality's decision "worrying" and planned to take up the matter with Israel.
"We will be reminding the Israeli government of its responsibilities to insure that provocative steps are not taken in the city, particularly at this fragile time," his spokesman Richard Miron said.
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