The United States helped defeat the resolution, which also demands an Israeli withdrawal from the occupied West Bank, in a Security Council vote on Dec. 30. Abbas said on Sunday he hoped to resubmit the resolution "perhaps after a week".
France, one of the Council's five permanent members, backed the resolution despite some reservations. France's parliament also backed Palestinian independence in a symbolic vote on Dec. 2 that underlined Europe's impatience with a stalled Middle East peace process.
But Paris signalled concern that Abbas' diplomatic offensive -- he has also signed up to 20 international conventions including the Rome Statute of the International Criminal Court -- could harm chances for peace by antagonising Israel.
"We are against the logic of letting this spiral (out of control)," Foreign Minister Laurent Fabius told reporters.
"While we think the Palestinians have the right to move the status quo, at the same time there has to be an effort to find a consensus solution. Once you set this cycle off, you get results that you don't want one way or another."
Abbas hopes that new countries which joined the U.N. Security Council on Jan. 1 will be more sympathetic to the Palestinian resolution, which demands an Israeli withdrawal from the occupied territories and independence by late 2017.
France had been working prior to the Dec. 30 vote on a separate resolution with Britain and Germany that aimed to set the parameters and a time frame for new peace talks.
"We worked on this resolution believing we could achieve a consensus but it wasn't possible," he said, indicating that France was likely to back a new Palestinian resolution provided the text remained broadly unchanged.
However, Fabius questioned the wisdom of resubmitting the resolution, adding he would discuss the issue in coming days with Jordan, Egypt and other regional players.
"The real question is to understand what is behind this move. Is it to get an American veto with a new U.N. Security Council composition? Is it to reaffirm an attitude towards the Israeli government? I don't know."
The United States, which has veto power as a permanent Council member, has pledged to block Abbas's plan, calling it one-sided and unproductive.