Nick Clegg has intensified his attacks on the Conservatives over welfare cuts by dismissing a proposal by Iain Duncan Smith to limit child benefit to the first two children as a "Chinese-style family policy".

Speaking on the Andrew Marr Show on BBC1, the deputy prime minister also warned that the Tories were locked in a "deathly embrace" with Ukip over Britain's membership of the EU. This would lead to a race to the bottom, he said.

Clegg opened up a new rift on a separate front with the Tories last week when he rejected a proposal by George Osborne for an extra £12bn in welfare cuts in the next parliament to help stabilise the public finances. The chancellor raised the prospect of withdrawing housing benefit from people under 25.

The deputy prime minister said he favoured eliminating the budget structural deficit by 2018 but Osborne was wrong to focus on cutting in-work benefits rather than raising taxes on the rich.

Duncan Smith, who is sceptical of Osborne's plan to withdraw housing benefit from those under 25, told the Sunday Times of a "brilliant" proposal to save £4bn by limiting child benefit to the first two children in a family. Clegg dismissed that when he told the Andrew Marr Show: "I will look at all proposals. But some of the ones I have seen floated – for instance the idea of a two-child policy. I am not in favour of penalising the young. I am not in favour of a sort of Chinese-style family policy saying the state says it is OK to have two children, it is not OK to have three children.

"Remember this is child benefit that goes to families, many of whom are working. They are working very hard, often on low incomes. My priority is a fair approach to ongoing fiscal consolidation. If you have to balance the books you mustn't balance the books only on the working-age poor."

The deputy prime minister also warned that the Tories were jeopardising Britain's position within the EU as he rejected a proposal in a letter supported by 95 Conservative MPs for the British parliament to be allowed to veto EU laws. Downing Street also gave a highly sceptical response to the letter, which was published in the Sunday Telegraph.

No 10 said: "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."

The deputy prime minister dismissed the letter. He said: "Conservative MPs now need to make up their mind. If they want full exit from the EU they should be free to argue it but then they should come clean.

"What they are 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. You can't safeguard a single market where British firms can export and trade into the rest of the EU if you are constantly saying you – the rest of the EU – have got to play by the rules but we won't. You are either in or out. You can't sort of be half in."

Clegg warned that the Tories were more widely "flirting with exit" from the EU which would be an "act of economic suicide". He said: "Politically we now have two parties – Ukip and the Conservative party – locked in this deathly embrace, this fight to the finish. My concern is what happens is they argue with themselves, they ratchet up the rhetoric in ever more breathless terms against the EU and our place in it.

"What ends up happening is you get a race to the bottom. You get a drift towards the exit. That then jeopardises millions of jobs in this country, it reduces our standing in the world."