"We will submit our project to the UN Security Council tomorrow (Wednesday)," Nimr Hammad, adviser to Palestinian president Mahmud Abbas, told AFP.
Another official said Kerry was told at a meeting in London on Tuesday that the Palestinians would go ahead as planned with their text calling for a withdrawal of Israeli troops from occupied Palestinian territory within two years.
Kerry told the Palestinian delegation that Washington would use its veto within the Security Council, he said of the meeting between the secretary of state and chief Palestinian negotiator Saeb Erakat.
The official, who asked not to be named, said the London talks had been "long and difficult but achieved results".
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If the United States uses its veto, Erakat told Kerry, the Palestinians would apply to join all international organisations and conventions, including the International Criminal Court, a move firmly opposed by Washington.
France is putting together a more nuanced version of a draft to the Security Council setting a two-year timetable for concluding a peace treaty, without mentioning an Israeli withdrawal.
Mohammed Shtayyeh, a member of Abbas's inner circle, said France had "accommodated" the Palestinians.
"We have merged. We don't have two texts now. There is one single text. We have happily accepted the French text when the modifications have been added," he said, without elaborating.
Shtayyeh said the United States wanted any draft resolution to be put off until after an Israeli general election in March but the Palestinians were "sick" of two-way negotiations with the Jewish state that had made no progress.