The Palestinians already declared independence unilaterally in 1988
The European Union has said proposals by the Palestinians to try to have the UN recognise an independent state in the West Bank and Gaza are "premature".
Swedish Foreign Minister Carl Bildt, whose country holds the rotating EU presidency, said the conditions were "not there as of yet" for such a move.
Israel has warned that any unilateral action could unravel past agreements.
The chief Palestinian negotiator has said they will seek recognition because of the failure to restart peace talks.
Saeb Erekat said they had few options left, because Israel was continuing to build Jewish settlements on territory it has occupied since the 1967 war.
Israel has offered to restrict the growth of settlements, but the Palestinian Authority has demanded that all construction is halted before it will again attend peace talks.
Close to 500,000 Jews live in more than 100 settlements built on occupied territory in the West Bank and East Jerusalem since 1967. They are illegal under international law, though Israel disputes this.
The impasse has led the Palestinian Authority President, Mahmoud Abbas, to announce that he will not seek re-election.
Speaking before a meeting of EU foreign ministers in Brussels, Mr Bildt said the Palestinian proposal was "clearly an act borne by a difficult situation, where they do not see any road ahead".
"I don't think we are there yet," he told reporters.
"I would hope that we would be in a position to recognise a Palestinian state but there has to be one first, so I think it is somewhat premature," he added.
But Mr Bildt said the 27-nation bloc, which is the biggest aid donor to the Palestinians and trains the PA's police force, still wanted to help.
"There is a need to look at all the initiatives that might be possible," he added. "We are discussing other steps in order to demonstrate our support for the Palestinian aspirations more clearly than we have done before."
The US government, which is Israel's chief ally and has a veto on the UN Security Council, also acknowledged Palestinian frustration but voiced opposition to the initiative.
"We support the creation of a Palestinian state that is contiguous and viable," State Department spokesman Ian Kelly said. "But we think that the best way to achieve that is through negotiations."
Mr Erekat said Arab foreign ministers had decided at a meeting in Cairo last Thursday to approach the UN Security Council, and that they would seek the support of the international community.
"We have not been negotiating for two states for 18 days or 18 months. For God's sake, we have been doing it for 18 years! Now it's a defining moment," he told the BBC on Sunday.
"Isn't it time now to define the two states? This is consistent with the terms of reference for the peace process because the respective Israeli governments have failed us in this."
But Israel threatened to retaliate if the Palestinians took such a step.
"Any unilateral movement will be countered by a unilateral move on our part," Foreign Minister Avigdor Lieberman said on Monday.
"We cannot conduct policy or negotiations unilaterally; it runs counter to all previous agreements and that's how we will treat it."
Correspondents say the Palestinian Authority's move reflects its growing frustration with the deadlock in the peace process, but it is largely symbolic.
The Palestinians already declared independence unilaterally in 1988. The move was recognised by dozens of states but not implemented.