JERUSALEM — Dov Hikind, a member of the New York State Assembly, was in this disputed city on Wednesday looking for property to buy. He said he was most excited about a new apartment complex overlooking the Old City called Nof Zion.

At noon, Mr. Hikind led a group of about 50 American Jews in laying a cornerstone for the next phase of Nof Zion, with construction scheduled to start next spring. “I want to buy here,” Mr. Hikind said. “I might make a deal while I am here this time.”

More than a real estate deal, though, it would be a statement: Nof Zion, a private Jewish project, is in Jebel Mukaber, a Palestinian Arab neighborhood of East Jerusalem, in territory Israel captured from Jordan in the 1967 war. Israel claims sovereignty over all Jerusalem; the Palestinians demand the eastern part as the capital of a future state.

Even within Israel, the idea of Jews moving into predominantly Arab neighborhoods of Jerusalem stirs heated debate. Two well-known Israeli families refused City Hall’s offer to name the street leading to Nof Zion for their deceased relatives, according to the local Jerusalem press.

But illustrating the complexity of the Jerusalem conundrum, others argue that Jews, Christians and Muslims should be able to live wherever they like. Not allowing Jews to live in certain neighborhoods of the city “is segregation,” said Mr. Hikind, a Democrat who represents several heavily Orthodox Jewish neighborhoods in Brooklyn.

With new tensions surfacing between the Obama administration and Israel over building in contested parts of Jerusalem, the city’s character and future remain central motifs in the stalled Israeli-Palestinian peace talks.

The cornerstone-laying ceremony at Nof Zion took place a day after the Israeli authorities moved ahead with plans for the expansion of Gilo, a Jewish residential district in south Jerusalem also on land captured in the 1967 war. The plans for 900 more housing units drew a sharp rebuke from the White House.

President Obama, speaking to Fox News from Beijing, said “additional settlement-building does not contribute to Israel’s security” and would make peace efforts harder.

“I think it embitters the Palestinians in a way that could end up being very dangerous,” he said.

From 1948 to 1967 Jerusalem was divided between Jordanian and Israeli control. It has been united, at least nominally, under Israeli control for the past 42 years. In that time, the parts of Jerusalem claimed by the Palestinians have turned into a patchwork of Arab and new Jewish neighborhoods, home to as many as 250,000 Palestinians and roughly 190,000 Jews.

As long as the populations live in separate quarters, advocates of two states, Israel and Palestine co-existing side by side, say a formula for an agreement on Jerusalem can still be found, with the Jewish areas administered by Israel and Arab areas placed under the control of the Palestinian authorities in the West Bank.

But critics charge that mingling the two populations will destroy the prospects for a two-state solution. As a first step toward resuming the peace process, the Obama administration and the Palestinian leadership had been trying to get Israel to halt all settlement activity to create a more conducive environment for talks. The Israeli government has offered to slow down construction, but not to halt it completely, and it refuses to include Jerusalem in any settlement freeze.

Mr. Hikind vociferously opposes the Obama stance, which means, he says, that Jewish residents “cannot build a toilet” in the West Bank. He said he was also for peace, only “unfortunately, it is not happening” right now.

Earlier this week his party toured the Jewish settlements of Samaria in the northern West Bank with a view toward buying houses or trailers to rent to settler families. On Wednesday morning, before the cornerstone ceremony, the group, which visited the settlements in a show of solidarity, toured Silwan and other Arab neighborhoods of Jerusalem where Jewish religious nationalists have moved in.

Nof Zion is built on privately owned land that an Israeli developer bought over the years. In the first stage of the project, 91 apartments were built, and 70 are already occupied. There are kindergartens, a small park with a jungle gym and plans for a domed synagogue.

Across town, in the Arab East Jerusalem neighborhood of Issawiya, the Israeli authorities on Wednesday demolished a Palestinian home that had been built without a permit. The security forces accompanying the bulldozers were pelted with stones. Several other unauthorized structures were taken down in other Arab areas, including Silwan.

When it comes to demolitions, Jerusalem’s City Hall says it applies the law equally in all parts of the city, regardless of religion or race. But officials acknowledge that the process of obtaining a building permit is costly and complicated. Most Palestinian residents do not qualify.

Many of them feel that the Israelis are trying to push them out. “In Gilo they are building; here they are demolishing,” said Abdul Halim Dari, 44, the owner of the destroyed house in Issawiya.