William Hague has flatly rejected demands from 95 Tory MPs for Parliament to be given a veto over all laws from Brussels.
The Foreign Secretary risked inflaming simmering Conservative tensions over Europe by branding the proposal "unrealistic" and warning it would make the single market unworkable.
The intervention came after backbenchers wrote to David Cameron saying the Commons should have the authority to block new EU legislation and repeal measures that threaten Britain's "national interest".
According to the Sunday Telegraph, signatories to the missive - drafted by senior MP Bernard Jenkin - include James Clappison, Conor Burns, John Baron, Anne Main and former defence minister Sir Gerald Howarth.
Another six apparently support the proposal but have not added their names - some because they are in government jobs.
Parliament currently has no automatic veto over EU laws, and the Prime Minister can only use the UK's veto to head off new rules in the most sensitive issues - such as defence and the budget.
A cross-party committee of MPs which scrutinises EU laws last month recommended that a national veto be introduced.
And the MPs' letter, sent to the Prime Minister this weekend, called on Mr Cameron to adopt the policy.
"Each time you have stood up for British interests in Brussels, you have achieved a great deal," it said.
"Building on your achievements, we would urge you to back the European Scrutiny Committee proposal and make the idea of a national veto over current and future EU laws a reality."
The letter stated that a new national veto over EU laws would "enable Parliament to disapply EU legislation, where it is in our vital national interests to do so".
It added: "This would transform the UK's negotiating position in the EU."
The letter said the veto - which would require a new Act of Parliament - could be used to deliver key reforms to Britain's relations with Europe. That could include gaining control over immigration from within the EU.
The MPs praised Mr Cameron for his insistence that national parliaments, not bureaucrats in Brussels, are "the true source" of democratic legitimacy in the EU.
"However, clarity about how we will achieve these objectives is vital for our credibility," the letter says.
Speaking on Sky News' Murnaghan programme, Mr Hague said his EU counterparts were in no doubt that the UK was seeking "more power for national parliaments, more accountability of the EU to national parliaments".
He said Britain had already proposed a 'red card' system which would allow groups of national parliaments to block unwanted measures from Brussels.
"On the specific (parliamentary veto) proposal... when you think about it of course if national parliaments all around the EU were regularly and unilaterally able to choose which bits of EU law they would apply and which bits they would not then the European single market would not work and even a Swiss-style free trade arrangement with the EU would not work," Mr Hague said.
"So we have to be realistic about these things."
A Number 10 spokesman said: "The Prime Minister set out his approach in his Bloomberg speech.
"He has already won his battle over European bank bailouts, cut the EU budget for the first time and launched a landmark debate on the future of freedom of movement.
"The Prime Minister is also the only one of the three main party leaders committed to giving the British people an in-out referendum on membership of a reformed EU.
"We will of course study this idea closely. But we need to look at what it would mean in practice.
"We've always been clear that Parliament is sovereign and more power for national parliaments must be a key part of a new settlement, including a 'red card' power so groups of national parliaments can block unwanted EU interference.
"But if individual national parliaments regularly and unilaterally overturned EU laws the Single Market wouldn't work, and even a Swiss-style free trade deal with the EU wouldn't be possible.
"It is important to negotiate a new deal for Britain in the EU and then put the choice to the British people: stay in the EU on new terms or leave altogether."
In an interview with the Sunday Times, Work and Pensions Secretary Iain Duncan Smith said he would like EU immigrants to have to wait for up to two years to claim benefits - rather than the current period of three months.
He said he had been speaking to other member states such as Germany, Italy and the Netherlands who were supportive of the idea.
According to Mr Duncan Smith, Britain should ask migrants to "demonstrate that you are committed to the country, that you are a resident and that you are here for a period of time and you are generally taking work a nd that you are contributing".
He added: "At that particular point . . . it could be a year, it could be two years, after that, then we will consider you a resident of the UK and be happy to pay you benefits."
Sources close to Mr Duncan Smith stressed that he was merely expressing an aspiration for the future, rather than spelling out a policy.
Mr Jenkin added: "The response by a spokesman for No 10 does not address how the PM can deliver his Bloomberg principle - that national parliaments should be the true source of democratic legitimacy and accountability in the EU.
"Nor does it acknowledge that the EU has claimed vastly more power in the name of the 'single market' than is necessary to promote trade and cooperation between its member states. We look forward to continuing discussions on these matters."
Speaking on the BBC's Andrew Marr show, Deputy Prime Minister Nick Clegg accused Tories of getting into a "race to the bottom" with the UK Independence Party (Ukip)
"We now have two parties - the UK Independence Party and the Conservative Party - locked in this sort of deathly embrace, this fight to the finish, and my concern is that actually what ends up happening is that they argue with themselves and they ratchet up the rhetoric in ever more breathless terms against the European Union and our place in it," the Liberal Democrat leader said. "Of course what ends up happening is that you get a race to the bottom. You get a drift towards the exit and that then jeopardises millions of jobs in this country."
He added: "Conservative MPs now need to make up their mind. If they want full exit from the European Union, they should be free to argue it, but then they should come clean because basically what they're saying is they want to have their cake and eat it: they want to be part of a European club but they don't want to play by the rules."
Mr Clegg also reiterated that the Lib Dems did not support a Tory backbench bid to pass legislation guaranteeing an in-out referendum on EU membership in 2017.
"Of course I know some people feel very strongly about this, but actually most people feel that the priority... should not be endless parliamentary games on Friday afternoons about when you do or don't hold a referendum when we've already got the guarantee about when a referendum will take place."
Mr Clegg compared the benefits of countries working together in Europe to those of England, Scotland, Wales and Northern Ireland co-operating as Britain.
And he said he believed the UK public would vote to stay in the EU. "I personally believe that when and if there is a referendum, I don't actually believe the British people will vote for exit," he said. "Not because people don't want the European Union to be reformed - I want it to be reformed, of course it constantly needs to be reformed - but because people know that in a globalised world... it's essential that we remain an outward facing, engaged, open trading nation."
Justice Secretary Chris Grayling expressed doubts about whether the letter was the right approach and said it was unrealistic for one parliament to be able to veto laws across the EU.
The Eurosceptic Cabinet minister said he understood his fellow Tories' concerns and said he supported the idea of a red card system.
Mr Grayling told BBC One's Sunday Politics: "I'm very clear, I think that we need a red card system in Europe for European law. The European Commission has just actually in my view treated the first example of a yellow card under the Lisbon treaty much too dismissively.
"I don't actually think it's realistic to have a situation where one Parliament can veto laws across the whole European Union. The Foreign Secretary has said that this morning.
"I understand the concerns of my colleagues but when we set out to renegotiate our membership, and we have got to deliver real renegotiation, we have also got to have a system that we propose which is viable and I'm not convinced we can actually have a situation where one parliament could prevent laws from happening right across the European Union.
"I'm not sure that this is the right approach. I absolutely support the idea of a red card system which allows national parliaments more broadly to say to the European institutions 'think again'."
George Osborne is expected to use a speech on Thursday to say Britain should remain in a reformed European Union.
Addressing a conference of the Tory Fresh Start group, the Chancellor will reportedly insist the UK is gaining support as it pushes for EU changes.
He is said to have held productive negotiations with German finance minister Wolfgang Schäuble and the Spanish government.