"It is time for the British people to have their say. It is time to settle this European question in British politics," the excerpts quoted Cameron as saying in London in a long-awaited address originally set for Friday in Amsterdam, the Netherlands. Cameron postponed the address because of the hostage crisis at an Algerian gas plant that resulted in at least three British deaths.
"I want the European Union to be a success. And I want a relationship between Britain and the EU that keeps us in it," Cameron states in the excerpts.
But a growing "gap" between the EU and its citizens "represents a lack of democratic accountability and consent that is -- yes -- felt particularly acutely in Britain," he says in the excerpts.
"If we don't address these challenges, the danger is that Europe will fail and the British people will drift toward the exit. I do not want that to happen," Cameron's speech excerpts said.
Britain's Conservatives now govern in a coalition with the Liberal Democrats. If the Conservatives are elected in 2015, they would renegotiate Britain's relationship with the EU, and then hold the referendum on the negotiated relationship around 2017, in the first half of the party's five-year parliamentary term, Cameron was expected to say.
"And when we have negotiated that new settlement, we will give the British people a referendum with a very simple in-or-out choice to stay in the EU on these new terms, or come out altogether. It will be an in-out referendum," he planned to say.
The Wall Street Journal said Cameron was betting his address would appease his party's Euroskeptic wing, which sees the EU taking power from member states, and, at the same time, keep Britain in the EU under new and better terms.
Cameron's pledge also depends on his party's winning the 2015 election and its being able to work out a treaty change with the 27-member EU, which will have 28 members after Croatia joins July 1.
No European or EU leaders had any immediate public comments ahead of his address.
France earlier warned privately that Britain would not be allowed to "cherry-pick" which parts of EU membership it would keep, the Journal said.
And allies of German Chancellor Angela Merkel have warned Cameron not to try to "blackmail" the rest of Europe by threatening to block future EU treaties, such as on the struggling eurozone, unless he wins a better deal for Britain, the Financial Times reported.
Some European officials have said they worry a British move could prompt other countries to try to follow suit.
In Washington, the White House Thursday quoted President Barack Obama as telling Cameron by telephone "the United States values a strong U.K. in a strong European Union, which makes critical contributions to peace, prosperity and security in Europe and around the world."
U.S. Ambassador to Britain Louis Susman told Sky News Sunday: "We cannot imagine a strong EU without a vibrant partner in the U.K. That is what we hope will come about, but it is up to the British people to decide what they want."
Britain, a close U.S. ally, is part of the EU but doesn't use the euro currency. It is one of the bloc's biggest economies and a key financial center.
No EU member state has ever left the union, although Greenland, an autonomous province of Denmark, withdrew from EU predecessor the European Economic Community in 1985.