The daily Yediot Aharonot said three battalions of reservists -- some 1,500 personnel -- have been mobilised and units already in the occupied territory have been reinforced.
On Friday, Israeli troops fired tear gas at rock-throwing Palestinian protesters at the village of Nabi Saleh, near Ramallah, but no casualties were reported.
Later, in a televised address to the Palestinian people from his Ramallah headquarters, Abbas declared: "We are going to the Security Council.
"When I have finished delivering my speech (to the General Assembly), I will submit the request for membership to the Secretary General to be passed to the president of the Security Council," he said.
"It is our legitimate right to demand the full membership of the state of Palestine in the UN," he said, "to put an end to a historical injustice by attaining liberty and independence, like the other peoples of the earth, in a Palestinian state on the borders of June 4, 1967."
He was referring to the lines that existed before the 1967 Six Day War, including Gaza, the West Bank and east Jerusalem.
Israel says they are indefensible and the borders of a future Palestinian state must be defined in bilateral negotiations.
It responded to Abbas by saying the UN bid would not bring the Palestinians peace, and slamming a reconciliation deal announced in May between Abbas's Fatah movement and the militant Islamist Hamas, which rules the Gaza Strip.
"Peace is not achieved by a unilateral approach to the UN, and not by associating with the Hamas terror organisation," said a statement from Prime Minister Benjamin Netanyahu's office.
"Peace will only be attained by direct negotiation with Israel," it added.
Hamas itself hit out at Abbas's strategy, to which it is not a party, saying it could weaken the campaign to allow Palestinian refugees back to their former homes and delegitimise armed opposition to Israeli occupation.
It "carries numerous risks and could violate national rights such as the right of return, the right of resistance and self-determination," said spokesman Sami Abu Zuhri.
The United States says the basis for an agreement should be the 1967 borders but with mutually agreed amendments.
Netanyahu says he will also go to the UN to explain Israel's opposition to the Palestinian move. Like Abbas, he is to speak on September 23, a government official said.
The White House says he is also likely to meet President Barack Obama in New York.
Washington has threatened to veto a Palestinian membership motion at the Security Council, saying it would harm prospects for peace talks and that a Palestinian state can only result from negotiations with Israel.
"We believe strongly that the road to peace and two states living side by side does not go through New York, it goes through Jerusalem and Ramallah," US Secretary of State Hillary Clinton said on Thursday.
Following Abbas's speech on Friday, Canadian Prime Minister Stephen Harper said his country would also oppose the Palestinan bid.
"Unilateral actions like this are unhelpful in terms of establishing peace in the Middle East," Harper told reporters. "Canada views the action as very regrettable and we will be opposing it at the United Nations."
On Thursday, UN Secretary General Ban Ki-moon called on the Palestinians to return to talks and that the peace deadlock was harming the whole Middle East.
"I am asking them to enter into meaningful negotiations and the international community has a duty to create some conditions favourable to this," he said.
Israeli newspaper Haaretz reported Friday that Israeli officials fear the Palestinians may launch legal action against settlements if their bid for upgraded UN status bears fruit.
It said that Netanyahu had on Thursday told diplomats of his concerns about a possible Palestinian recourse to the International Criminal Court in The Hague over the settlers issue.
It said he expressed his fears at meetings with US, EU and Quartet envoys who have been meeting Israeli and Palestinian leaders in an effort to get them back into direct peace talks that stalled a year ago.
A senior Israeli government official said a Palestinian ICC challenge "would be worrying, given that it would demonstrate that they seek to perpetuate conflict instead of seeking peace."
But the official also believed that "Israel has little to worry about in this case as it has not ratified the Treaty of Rome recognising the authority of the ICC, and is not therefore bound to implement its rulings."
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