But there are no easy questions in the Israeli-Palestinian conflict. Mr. Abbas’s answer, in an interview broadcast on Israeli television on Friday night — yes, he would like to visit, but not to live there; Safed is part of Israel — was widely interpreted as a surprising concession on the demands of Palestinians to return to their pre-1948 homes, perhaps the most intractable and emotional of all the unsettled issues in the decades-old dispute.

The remark set off angry protests across the Gaza Strip, in which demonstrators set Mr. Abbas’s picture aflame. Palestinian rivals and commentators denounced him as a traitor, or worse. In Israel, the response was strong if mixed, and the issue dominated political chatter on Sunday after weeks in which the Palestinian question had been all but absent from the debate ahead of the Jan. 22 elections.

President Abbas himself beat a hasty retreat. In an interview with an Arabic newspaper published Sunday, he said he was talking only of his personal aspirations, not about giving up anyone’s rights, and called the refugees “a sacred matter” that could be resolved only as part of a larger agreement through negotiations.

The controversy could further complicate Mr. Abbas’s planned bid for nonmember statehood at the United Nations General Assembly this month, a move that has generated intense opposition from Israel and the United States but that has failed to generate much enthusiasm among his own people. His popularity had already nose-dived over the past year amid a stalemate in the peace process, severe budgetary shortfalls, a worsening rift with the rival Hamas faction that controls Gaza and growing dissent within his own party, Fatah.

“He has been doing many mistakes, and this is one of them — his vocabulary was totally wrong,” said Mahdi Abdul Hadi, chairman of the Palestinian Academic Society for the Study of International Affairs, based in Jerusalem. “He underestimated the reaction; he underestimated the anger and the frustration in the society; he underestimated his constituency. It’s very clear that he’s not the hero, he’s not the liberator, he’s not the leader.”

There are about five million Palestinians scattered around the world who are descendants of the 750,000 who lost homes during the war that led to Israel’s establishment, many of them still clutching keys in hopes of someday returning. But Israelis see such ambitions as an existential threat to their state, and negotiators have tried to distinguish the moral question of the “right of return” from the practical one. Documents released in 2011 show that the two sides have traded numbers about how many Palestinians would be allowed into Israel, ranging from 5,000 to 100,000, and that Mr. Abbas himself said in 2009 that “it is illogical to ask Israel to take five million, or indeed one million.”

Mkhaimar Abusada, a political scientist at Al Azhar University in Gaza City, said Palestinians “are willing to make big compromises on the right of return,” but only in exchange for a state along the 1967 borders with East Jerusalem as its capital (a point that Mr. Abbas emphasized in the television interview, though it was largely lost in the frenzy over his Safed remark).

“Unless there is a final peace settlement with Israel,” said Mr. Abusada, himself the child of refugees from a village near the Gaza Strip, “they are going to keep holding onto these keys, to keep holding onto these memories.”

Khalil Shikaki, director of the Palestinian Center for Policy and Survey Research, in theWest Bank, said his polls had consistently shown that a majority of Palestinians would support a deal in which only a fraction of the refugees, 100,000 or 150,000, were allowed back. But 30 percent see the right of return as their “most vital goal,” second only to the establishment of a Palestinian state, according to the most recent survey, in September.

“This is a battle over narrative,” Mr. Shikaki explained. “Normally when people say something along the lines of what he said, they would distinguish that from the right of return. He’s now essentially given Hamas an opportunity to try and use this occasion to mobilize against him.”