Condoleezza Rice, the US secretary of state, and Tzipi Livni, Israel's foreign minister, told Mahmoud Abbas in separate talks in New York on Monday that there could be no compromise on the three principles that had been set by the quartet of Middle East mediating states in January.
Saeb Erikat, a close associate of the Palestinian leader, said: "Secretary Rice was very clear about the need to see the three quartet principles without anything else."
Livni said: "From Israel's perspective, there is a need for any future Palestinian government to meet completely the three requirements of the international community."
Erikat said Abbas had reassured Livni that the national unity government he was negotiating with Hamas would recognise Israel's right to exist.
Among the issues discussed between Abbas and Livni during an hour of talks was the release of abducted Israeli soldier Corporal Gilad Shalit, which Livni called "the most important issue for Israel".
Erikat said he hoped the Israeli soldier could soon be released along with Palestinian prisoners held by Israel, but that he did not want to talk about the efforts to free them because it could derail a deal.
Livni would not comment on whether she discussed with Abbas a possible deal for the release of the soldier in exchange for Israeli agreement to free hundreds of Arab prisoners.
The Israeli foreign minister confirmed that Israel wanted to maintain a dialogue with Abbas in order to get Hamas to moderate its anti-Israeli views.
"I don't see this as one meeting and each side checks off a box and goes home. The idea is to establish a permanent channel of dialogue," she said.
Her remarks indicated that Israel is interested in renewing contacts that have been largely frozen in recent months after Hamas was elected to power in January.
Livni said said that while Israel had postponed its plan to withdraw from large areas of the West Bank for the time being, her government was still interested in advancing the US-backed road map plan that outlined the formation of a Palestinian state.
Public support in Israel for such a West Bank pullback fell considerably after fighters allied with Hamas kidnapped Shalit at an army base just inside Israel.