Jerusalem (CNN) -- Hundreds of Hamas supporters took to the streets of Gaza on Saturday, protesting against Palestinian Authority President Mahmoud Abbas and accusing him of giving up a key demand from Israel: a so-called "right of return."
Abbas, however, said he did no such thing. And a Palestinian official accused Hamas of trying to undermine Palestinian Authority efforts at the United Nations
Abbas leads the Palestinian Fatah movement based in the West Bank, which has battled Hamas for power.
Over the weekend, in an interview with Israel's Channel 2, Abbas spoke about being originally from the town of Safed in northern Israel.
He said he would want to go back to visit, but not to live.
"I want to see Safed. It's my right to see it, but not to live there," he said. "Palestine now for me is '67 borders with east Jerusalem as its capital," he added, referring to the borders that existed before the 1967 war.
"I believe that West Bank and Gaza is Palestine, and the other parts is Israel."
Many Palestinian officials have generally argued that Palestinians should have a right to return to their ancestral homes in what is now Israel.
Hamas leader Salah al-Bardawil, speaking at one of two Hamas rallies Saturday in Gaza, said Abbas "must apologize to the Palestinian people" for his remarks. Protesters trampled on posters of Abbas, saying he had abandoned the demand for a right of return.
But Abbas insisted that he was only speaking for himself.
Palestinian state-run news agency WAFA carried a quote from an Abbas spokesman saying that whoever "accepts a temporary state is the one who gives up the right to return."
That idea has long been suggested: that Palestinians who would choose to live in an independent Palestinian state would give up demanding a right of return.
Saeb Erakat, a member of the executive committee of the Palestine Liberation Organization, told CNN,"Hamas taking to the streets and doing all of this is an attempt to undermine the PLO and our attempt to go to the U.N.," where the Palestinian government plans to push for Palestine to become a nonmember state based on 1967 borders. Erakat said Hamas was "sabotaging" those efforts.
The Palestinian Authority is made up of PLO committees.
"We are not going there to confront the Americans or to isolate Israel," Erakat said of his government's U.N. plans. "We are going there to support and facilitate the two state solutions and to sustain the two state solution."
Israeli Prime Minister Benjamin Netanyahu on Sunday said he had seen the televised interview with Abbas, and heard that he "has already gone back on what he said. But this only proves how important it is to get into direct negotiations without any preconditions. Only direct negotiations will allow us to clarify what the true positions are."
Netanyahu added that if Abbas "is indeed serious and intends to push the peace process forward, as far as I am concerned, we can sit together immediately. Jerusalem and Ramallah are seven minutes apart. I am prepared to start the talks today."
He called on Abbas "to return immediately to the negotiating table without conditions."
CNN's Kareen Khadder, Talal Abu Rahma, and Josh Levs contributed to this report.