The Palestinians have so far enlisted the support of at least six or seven members of the Security Council, a senior official said Tuesday DPA reported.
They are trying to convince two or three more Security Council members to vote in favour of recommending that Palestine be accepted as a UN member state, Palestinian Foreign Minister Riad Malki said.
Meanwhile, Israeli Prime Minister Benjamin Netanyahu, ahead of his scheduled departure to the General Assembly session late Tuesday or early Wednesday, called on Abbas to meet with him in New York.
"I call on the Chairman of the Palestinian Authority to open direct negotiations in New York, which would continue in Jerusalem and Ramallah," he said in statement from his Jerusalem office.
"I propose to President Abbas to begin peace negotiations instead of wasting time on futile unilateral measures," he said.
But Abbas confirmed to UN Secretary-General Ban Ki-moon in New York Monday that he planned to submit his application for full membership on Friday, immediately after his address to the General Assembly's 66th session.
He told Fox News he was willing to meet Netanyahu in New York, but for the protocol, not to relaunch negotiations.
Abbas has conditioned negotiations on an Israeli construction freeze in the occupied West Bank and East Jerusalem. Netanyahu insists on negotiations without preconditions. The last round of talks broke off one year ago.
Working frantically ahead of Friday, when President Mahmoud Abbas plans to submit the membership application, Palestinian diplomats hope to achieve a moral majority of nine, so that the US will have to use its veto.
Washington meanwhile, is working feverishly to muster a blocking minority of seven, so that it will not have to use its veto.
For any decision to pass in the 15-member Council, nine "yes" votes are needed, and no "no" vote by a veto power.
China, Russia, Lebanon, South Africa, Brazil and India are expected to vote in favour.
Malki said that while the Palestinians have support from six of the 15 Security Council members, three states - Gabon, Nigeria and Bosnia Herzegovina - remain undecided.
He said the Palestinians are exerting pressure on these three countries to support the Palestinian effort, explaining that Gabon seems to have made up its mind to support the Palestinian bid, but the other two remain hesitant.
Israel's ambassador to the UN, Ron Prosor, said Monday that Portugal was also still undecided.
Malki said the Palestinians hoped to get nine members behind them as soon as possible to ensure their application could be discussed in the next few days, even if "the US is going to veto it and embarrass itself."
He said Abbas was under heavy pressure not to submit the application.
Abbas met Ban in New York Monday, shortly after his arrival from Amman.
Ban informed Abbas of what was needed to be attached to the application to make it valid, Malki said.
He said the Palestinians worked all day Monday to get these additions ready by Friday.
Abbas also met European foreign policy chief Catherine Ashton, as well as the Norwegian and French foreign ministers.
Netanyahu, meanwhile, is scheduled to meet President Barack Obama in New York before noon Wednesday. No face-to-face meeting has been scheduled so far between Abbas and Obama.
Europe is trying to convince Abbas not to go to the Security Council, but to the General Assembly, for a watered down request.
"The president was clear in his position," Malki said.
"He told them that we are committed to going to the Security Council to get full UN membership and we will not accept anything less," the Palestinian foreign minister told Voice of Palestine Radio.
The Palestinians will ensure that Abbas receives a warm welcome in the General Assembly and loud applause after almost every sentence in his speech, he vowed.
A large demonstration is planned outside the UN building in New York in support of Abbas and the Palestinian bid. Malki said he expected thousands to participate.