David Cameron has said there will be no retreat on deficit reduction - and that he was right to speculate publicly about the break up of the euro.
He told business leaders in Manchester that it was "more dangerous to stay silent than to speak out".
The prime minister later discussed the crisis with other European leaders including Angela Merkel and new French President Francois Hollande.
Labour says the recession is caused by coalition policies not the euro crisis.
Mr Cameron raised eyebrows at Prime Minister's Questions on Wednesday when he warned the eurozone it "either has to make up or it is looking at a potential break-up".
Chancellor George Osborne has repeatedly warned against speculating about eurozone break-up, saying it would cause instability amid Greece's ongoing inability to form a government able to push through austerity plans.
But he told MPs earlier on Thursday that the Greek elections had "let the genie out of the bottle" and "some of the things we were happy to say in private we are now also willing to say in public because the issue is out there".
"We have very clear ideas about what the eurozone needs to do to make their currency work," he added, saying he backed austerity measures in "peripheral" countries but also wanted to see the "core of the eurozone" do more "to support demand".
Mr Cameron discussed the eurozone situation with Mr Hollande, Mrs Merkel, Italian Prime Minister Mario Monti and EU officials in a conference call ahead of the forthcoming G8 summit in the United States.
The BBC's political editor Nick Robinson said the prime minister had reiterated the importance of decisive action to sort out the eurozone and to prevent contagion and repeated the key points of his speech.
But he said No 10 had refused to say whether Mr Cameron used the phrase "make up or break up" during the 45-minute conversation.
Downing Street has disclosed that the National Security Council has been involved in contingency planning in case of a worsening situation in Greece and the eurozone.
A spokeswoman said the Treasury had been drawing up contingency plans "for some time" but when asked whether there'd been any planning to deal with "civil strife" she said: "Certainly the national security council has, in the past, looked at issues regarding the eurozone."
In his speech in Manchester, Mr Cameron said it was "essential to speak out about what needs to be done to safeguard the eurozone, to safeguard Britain, to take the steps to make sure we deliver the strong and stable economic growth that we want".
Describing the situation in Greece as a "crisis that never really went away", he said the eurozone could find itself in "unchartered territory" unless it took steps to strengthen its banks and protect its weaker members.
"As I have consistently said it is in Britain's interest for the eurozone to sort out its problems," he said.
"But be in no doubt: whichever path is chosen, I am prepared to do whatever is necessary to protect this country and secure our economy and financial system."
He defended the coalition's austerity measures, saying the programme of spending cuts, tax rises and pay freezes was already having the desired effect of reducing the deficit.
"Let me be clear, we are moving in the right direction - not rushing the task but judging it carefully. And that is why we must resist dangerous voices calling on us to retreat.
Earlier, Business Secretary Vince Cable said Britain "shouldn't be panicking or be unduly negative" about the crisis in the eurozone.
"We need to get the risks in perspective," he told BBC Breakfast, adding there was no reason the crisis should spread beyond Greece.
But Labour said the UK government had become a "bystander" to events in Europe.
"David Cameron isn't part of the solution, he is part of the problem," opposition leader Ed Miliband said. "He promised Britain there would be recovery and he has delivered a recession.
"All of Europe's leaders, including David Cameron, bear responsibility for the fact that over the last two years they haven't sorted out the problems of the eurozone and they haven't had a proper plan for growth and jobs."