"The Americans will not be able to live with the text of the proposed Palestinian bill for the UN Security Council and therefore the version will not be advanced," Livni was quoted as saying by Israeli news website Ynet.
A leading member of Palestinian Authority President Mahmoud Abbas' Fatah movement told The Anadolu Agency that the movement "came under considerable pressure from the U.S. and the European Union to postpone the submission of the draft resolution."
On Monday, Israeli Prime Minister Benjamin Netanyahu met U.S. Secretary of State John Kerry in Rome in a bid to ensure American support in blocking any UN move setting a deadline for Israel to end its occupation of the Palestinian lands.
Neither official commented on the discussions that took place at the Villa Taverna, the residence of the U.S. ambassador to Italy.
However, American sources said that Kerry had stopped short of accepting Israel’s demand for a U.S. veto of the resolution, telling Netanyahu that Washington would continue to attempt mediation in the Middle East conflict.
The Palestinian Authority announced on Sunday its intention to present, through Jordan's UN representation, the resolution at the Security Council and to put the resolution to a vote as early as Wednesday.
Palestine's UN mission, however, said it was more likely that the text would be submitted on Wednesday, meaning that it is not certain when it will be brought to vote.
The Palestinian draft resolution will seek to apply the "two-state solution," providing the Palestinians with an independent state within pre-1967 borders with East Jerusalem as its capital.
The motion requires a “yes” vote of at least nine of the 15 council members to pass, but it can be vetoed by any of the permanent members, including the United States, a staunch ally of Israel.
Meanwhile, an alternative UN Security Council proposal which calls for a resumption of peace talks between Israelis and Palestinians within two years is also being discussed.
Kerry is said to be determined to seek support for the French-led proposal to present a compromise resolution at the Security Council. This resolution would push towards restarting negotiations, and promote a two-state solution without setting any deadline for Israeli withdrawal from the occupied Palestinian territories.
U.S.-brokered direct Palestinian-Israeli talks came to a halt in April because Israel refused to release a group of Palestinian prisoners despite earlier pledges to do so.