Some say Abbas has stepped up efforts to reconcile with Gaza's leaders. On Feb. 7, he sent four senior Fatah members to Gaza for talks, a gesture Hamas Prime Minister Ismail Haniyeh greeted as "a good step in the right direction."
American negotiators won't discuss their strategy as it relates to Hamas. But one U.S. official who spoke on condition of anonymity because he wasn't authorized to comment publicly said Abbas' role in the peace talks "has shown that he is willing to make courageous decisions that he believes are in the interests of the Palestinian people."
"By working to achieve an independent Palestinian state, President Abbas stands in stark contrast to Hamas, which is still a designated Foreign Terrorist Organization and is not serving the best interests of the Palestinian people," the official said.
Analysts say that no matter the pressures, Hamas is unlikely to agree to support a deal that requires recognition of the Jewish state and bars a Palestinian right of return. Doing so could isolate Hamas from a core constituency: refugees who oppose a two-state solution.
"The only solution is me going back to my home," said Hissi, the Gaza resident who believes Hamas should have a seat at the negotiating table. His father fled his village just east of the Gaza border during Israel's 1948 war for independence.
Hamas is not the only Palestinian group to oppose Abbas' negotiations.
Several parties that belong to the Palestine Liberation Organization, an umbrella group of which Fatah is the largest member, have also expressed their opposition to the peace talks, along with more radical militant groups and even some members of Abbas' party.
In a post on the website of the Gatestone Institute, a foreign affairs think tank, Arab-Israeli journalist Khaled Abu Toameh said some Fatah supporters were calling for the renewal of an "armed resistance" against Israel in Arabic-language interviews.
"Kerry needs to listen to what Hamas and other groups are saying in Arabic," Toameh wrote.
In Gaza, a leader of one of the militant groups blamed for firing rockets into Israeli territory said his organization rejects the talks and "will never accept anything but the full historical Palestinian lands."
"You cannot negotiate with the occupier," said Abu Ahmad, a spokesman for Islamic Jihad, who works from a Gaza City office decorated with framed photographs of men killed in battle with Israel. "What was taken by force will be retaken by force."
Special correspondent Rushdi abu Alouf contributed to this report.hdi abu Alouf contributed to this report.