The majority of people in the UK, France and Germany want their governments to vote in favour of recognising a Palestinian state if a resolution is brought before the United Nations in the next few weeks, according to an opinion poll.

The three European countries are seen as crucial votes in the battle over the Palestinians' bid for statehood at the UN, which meets next week. All three are pressing for a return to peace negotiations as an alternative to pursuing the statehood strategy, but they have not declared their intentions if it comes to a UN vote.

In the UK, 59% of those polled said the government should vote in favour of a UN resolution recognising a Palestinian state alongside Israel. In France and Germany, the figures were 69% and 71% respectively. Support for the Palestinians' right to have their own state, without reference to the UN vote, was even higher: 71% in the UK, 82% in France and 86% in Germany.

The poll was conducted by YouGov on behalf of Avaaz, a global campaigning organisation that is conducting an online petition in support of a Palestinian state. It is planning to deliver more than 913,000 signatories backing what it describes as "this new opportunity for freedom" to the European parliament .

David Cameron must listen to the views of the public, said Ricken Patel of Avaaz. "The prime minister has a clear choice: stand with the British public and 120 other nations to support a Palestinian state and a new path to peace, or side with the US government, which continues to push for a failed status quo."

The Palestinians appear to be assured of a majority if a resolution is put before the UN general assembly, whose annual session begins in New York next week. However, full membership of the UN requires security council approval, which the US confirmed last week it would veto.

The Palestinians may then seek "observer state" status at the general assembly, which is less than full membership but an advance on their current "observer entity" status.

The US, which is anxious to avoid wielding its veto and potentially incurring the wrath of Arab countries, is pushing for a return to negotiations – a move also supported by the EU, which is keen to avoid a damaging split among its 27 countries.

European foreign ministers are meeting in Brussels on Monday to discuss a common position on Palestinian statehood. Britain and France have said they would prefer to see meaningful negotiations on the basis of the pre-1967 borders with agreed land swaps, but have hinted they may vote for enhanced status for the Palestinians without such a prospect.

Germany is thought to be opposed the Palestinian plan, but on Friday the chancellor, Angela Merkel, said: "I am not going to disclose today our voting intentions, whatever they may be." She added that Germany was wary of unilateral moves. "We are going to use the days that remain to perhaps achieve a few millimetres of movement," she said.

The UN secretary-general, Ban Ki-moon, backed the idea of a Palestinian state last week. "I support … the statehood of Palestinians, an independent, sovereign state of Palestine. It has been long overdue," he said in Canberra.

Israel acknowledges that it has almost certainly lost the battle for votes at the general assembly. Ron Prosor, its ambassador to the UN, said last week: "This is a diplomatic endeavour against all odds ... It is clear to me that we can't win the vote." Instead, Israel was concentrating on securing a "moral minority" of powerful countries, which it hopes will include the EU bloc.

• The Avaaz poll, carried out by YouGov in the UK and Germany, and Ifop in France, was conducted online, with 2,552 respondents in the UK, 1,017 in Germany and 1,011 in France.