The plan, backed by the Arab League, has also been rejected by Washington, which along with the EU backs a negotiated solution to the Israeli-Palestinian conflict.
Mahmoud Abbas, the Palestinian president, said after meeting Hosni Mubarak, the Egyptian president, on Tuesday that the impasse in negotiations with Israel had left him with no option but to ask for a UN endorsement of statehood.
"The proclamation of a Palestinian state should be the result of the resistance putting an end to the occupation"
Hamas political leader
"The matter of the declaration and the matter of going to the Security Council is not a unilateral decision," he said.
"The decision emanates from an Arab follow-up committee [of the Arab League] that was convened recently ... and which agreed to go the Security Council for it to say that it supports an independent Palestinian state."
However, the plan has also been opposed by the Palestinian Hamas movement, which has failed to reach an agreement to end the political deadlock with Abbas's Fatah party and effectively rules the Gaza Strip.
Khaled Meshaal, the exiled Hamas political leader, said that in order to form a Palestinian state "our people must put an end to the occupation".
"The proclamation of a Palestinian state should be the result of the resistance putting an end to the occupation ... and not a decision taken by [the Palestinian Authority] to fill the void after the political option has failed," he said in a statement from Damascus, the Syrian capital.
The Israeli government has threatened to nullify past accords with the Palestinians if they take any unilateral action.
Avigdor Lieberman, Israel's foreign minister, said any Palestinian move on independence "will be countered by a unilateral move on our part".
Benita Ferrero-Waldner, the EU's external relations commissioner, said the bloc's foreign ministers were discussing ways to involve the US in helping to push Palestinians and Israelis to back peace talks.
"The most important thing until now is to really help the Americans bring both sides to the table," she said.
Bildt said he could understand why the Palestinians were suggesting such a move, as a way to break the current deadlock.
"It is clearly an act borne by a difficult situation where they don't see any road ahead and I can understand that," he said.
Negotiations between Israel and the Palestinians since Israeli forces began a 22-day war in the Gaza Strip last December.
Abbas has refused to return to the table with the Israelis until they commit to halt the all construction of illegal settlements in the occupied West Bank and East Jerusalem.
Bildt reiterated EU calls that Binyamin Netanyahu, the Israeli prime minister, move to freeze all building in the West Bank.
Netanyahu, who refuses to halt settlement construction, has urged the Palestinians to return to the negotiating table without conditions.