Gaps between Israeli and Palestinian negotiators only have widened in seven months and an extension of talks appears unlikely after what is bound to be a missed April 29 deadline for a framework deal, an aide to Palestinian President Mahmoud Abbas said Thursday.

Mr. Abbas will meet U.S. President Barack Obama March 17 as the U.S. tries to press both sides to agree on a framework or the ground rules for future negotiations. Mr. Obama had talks with Israeli Prime Minister Benjamin Netanyahu at the White House this week.

Mohammed Ishtayeh, the Abbas aide, laid out the two sides’ negotiating positions and the expected U.S. proposal for a framework deal.

“What we have seen in the talks is that the gap is growing, rather than narrowing,” said Mr. Ishtayeh, who resigned as a negotiator in November to protest accelerated Israeli settlement building.

For the Palestinians, the biggest obstacle is a new demand — introduced only in this round of negotiations — that they accept Israel as a Jewish state, he said. The Palestine Liberation Organization recognized the state of Israel when peace efforts began two decades ago and Mr. Abbas has argued this is sufficient.

Mr. Abbas cannot “under any circumstances” recognize Israel as a Jewish state because this would restrict the return options of Palestinian refugees and potentially pave the way for a gradual expulsion of Israel’s large Arab minority, Mr. Ishtayeh said.

Israel argues such recognition would prove the Palestinians are serious about peace.

Israel’s land demands pose another serious obstacle, Mr. Ishtayeh said.

The Palestinians want a state in the West Bank, Gaza Strip and east Jerusalem, lands Israel captured in 1967, but are ready to accept minor modification to accommodate some of the dozens of settlements Israel has built on occupied lands.

Israel wants to annex these “settlement blocs,” but never has presented a detailed border proposal. The Palestinians say these blocs add up to about 12% of the West Bank. Israel also wants a long-term military presence in the Jordan Valley, which makes up 28% of the West Bank.

Israeli officials have declined to discuss the content of the negotiations.

With U.S. Secretary of State John Kerry apparently unable to bridge the gaps, there is some expectation the U.S. will seek to extend the talks until year-end.

Mr. Ishtayeh said he believes this would be pointless because there is no common ground. “We don’t have terms of reference … which means we and the Israelis are reading from different books,” he said.

An Abbas aide suggested the Palestinian leader might agree to an extension with the right enticements. Ideas such a settlement freeze and a release of additional Palestinian prisoners by Israel have been floated.