Britain is "sleepwalking" into leaving the EU, which would undermine the UK's economy and leave it "voiceless and powerless," Ed Miliband has said.
The Labour leader argued that pro-Europeans could not turn a "blind eye" to the EU's failings.
A new approach should be based on "building alliances for change," he told the CBI conference.
But the Conservatives accused Labour of "opportunistic posturing" and not being "remotely credible" on the EU.
The prime minister, who is due to take part in EU budget talks this week, is also facing pressure within his own party, with Tory MP David Davis making a speech calling for a referendum that would allow the government to forge a new, looser relationship with Brussels.
Mr Davis said he would bet a "large sum of money" that the UK would leave the EU within a decade, without "maximum possible change" in the relationship with Brussels.
Last month, Labour MPs joined Tory rebels - including Mr Davis - to defeat the government on its strategy to push for a freeze in the EU budget, instead pushing for a real-terms cut between 2014 and 2020.
The prime minister insists that a freeze is more realistic, but he has threatened to use the UK's veto if the 5% rise proposed by the European Commission is not drastically reduced.
Labour's decision to vote for an EU budget cut was seen as evidence that the party is repositioning itself on Europe towards a more Eurosceptic position, but Mr Miliband said he "passionately believes that Britain is stronger in the European Union".
He warned the UK faced a "very dangerous moment" in its relationship with Europe and Mr Cameron, who has previously faced pressure from his own MPs to back an in/out referendum after the next election, was not working in the national interest.
Mr Miliband told the CBI conference in central London: "For more than three decades our membership of the European Union has seemed to be a settled question. Not any more. Public scepticism about European union has been on the rise for some time.
"Some cabinet ministers in this government now openly say that we would be better off outside the EU.
"And many of our traditional allies in Europe clearly think that Britain is heading to the exit door.
"Those of us, like me, who passionately believe that Britain is stronger in the European Union cannot be silent in a situation like this.
"I will not allow our country to sleepwalk toward exit because it would be a betrayal of our national interest."
Mr Miliband stressed the importance of being part of the single market for British businesses, which do 60% of their trade with EU members.
"If we left the EU it would be the United States, China, the European Union in the negotiating room - and Britain in the overflow room.
"We would end up competing on low-wages and low-skills: an off-shore low-value economy, a race to the bottom," he said.
The Labour leader argued the case for the EU was not served by ignoring the institution's "failings", adding that said the case for continued involvement had to be made "in a new way", rather than treating it as an "article of faith".
Instead, he argued for an approach based on "building alliances" with like-minded countries, based on plans for jobs and growth, reforming the EU budget, completing the single market and changing rules on competition.
But David Cameron described himself as a "good European", a "sensible, pragmatic British politician", who had "the people of Europe on his side" for campaigning for a tighter EU budget this week.
The prime minister told the CBI it "wasn't credible" to have cuts at home but then see the EU budget "going up and up", which he compared to "picking the pockets" of Europe's citizens.
Ken Clarke, the minister without portfolio and one of the most pro-European members of the government, accused Mr Miliband of acting "opportunistically", by voting with "extreme Eurosceptics" over the EU budget.
And Conservative chairman Grant Shapps said: "In a speech to business, Ed Miliband had the chance to detail how he'd deal with the deficit that Labour left behind. Instead, what we got was opportunistic posturing on Europe which isn't remotely credible."