A small group of ultra-right-wing Israelis marched through a volatile neighborhood of East Jerusalem on Sunday, arousing passions over the future of the contested city as an American envoy wrapped up an inconclusive three-day visit aimed at getting peace talks under way.

The Obama administration’s Middle East envoy, George J. Mitchell, met with Israeli and Palestinian leaders over the weekend in an effort to reach understandings that will allow the start of indirect, American-brokered negotiations.

Officials revealed few details about the discussions, but Mr. Mitchell described them as “positive and productive” and said he would return to the region next week.

Israel’s prime minister, Benjamin Netanyahu, said that Israel and the United States wanted to begin the peace process “immediately” and that its prospects would become clear “in the coming days.”

An Israeli official, speaking on the condition of anonymity, said that “the feeling is that we are back on track.”

But the Palestinians’ agreement to join the talks still depends on backing from the Arab League. After meeting Mr. Mitchell on Saturday, Saeb Erekat, the chief Palestinian negotiator, suggested that any announcement of talks might take another week or two.

The peace efforts were derailed last month after the Israeli announcement of plans for 1,600 new apartments in a Jewish neighborhood of East Jerusalem. The Palestinians have demanded an end to all Israeli settlement building, including in East Jerusalem, which they claim as their future capital, as a precondition to direct talks.

Mr. Netanyahu has rejected any building freeze in East Jerusalem, and the announcement, during a visit here by Vice President Joseph R. Biden Jr., strained Israel’s relations with the United States.

But on Sunday it was another neighborhood of East Jerusalem that illustrated the complexities and conflicting interests that define the city. About 40 far-right nationalists marched through the Wadi Hilwe section of Silwan, a predominantly Arab neighborhood, waving Israeli flags in a demonstration of Israeli sovereignty.

Wadi Hilwe sits on what Jews believe to be the ruins of the biblical City of David, in the shadow of the Temple Mount, or the Noble Sanctuary, a site holy to both Muslims and Jews. In recent years a Jewish settler group has sponsored excavations in the area and acquired property that is now populated by hundreds of Jews.

Itamar Ben-Gvir, one of the rally’s organizers, said it was a chance to show Mr. Mitchell “who is the boss in Jerusalem.”

“The Americans think they have a puppet in the Israeli prime minister’s office,” he said. “We are not puppets. Jerusalem is ours.”

But opposition to the march came from some unexpected quarters. Although the Israeli authorities permitted the march, for up to 70 people, those opposing it on grounds that it was a provocation included the Israeli prime minister’s office and the City of David settlement group. They failed in their efforts to have it postponed.

Hundreds of armed police officers secured the route and the surrounding area, both to protect the demonstrators and to contain them.

Israeli leftists and international activists joined Palestinian counterdemonstrations along the way. Palestinian families came out onto balconies and rooftops, beating on drums, banging metal saucepans and lids together, and chanting “God is great,” trying to drown out the rightists’ songs. Elsewhere in Silwan, clashes broke out between stone-throwing Palestinians and the police.

Dimitri Diliani, a Jerusalem representative of Fatah, the mainstream Palestinian movement, said the march proved that despite Israel’s claim on the area, it did not have sovereignty there.

“Where else in the world would you need 2,000 armed, fully equipped police officers to secure a failed march of 70 of your own citizens in an area that you claim as your capital?” he asked.