David Cameron will warn of "perpetual stagnation" if the eurozone crisis is not resolved in a speech in Mexico later, despite yesterday's pro-bailout result in Greek elections.
The prime minister, in the coastal resort of Los Cabos for the G20 summit, will tell a group of 300 senior company bosses he fears the challenge is as much one of "political will as of economics".
The summit follows yesterday's Greek elections in which the pro-bailout New Democracy party won a two-point majority over Syriza, which had campaigned against austerity.
"If a country wants growth in its national economy, then it has to deal with its debts, and dealing with its debts is every bit as essential as for the global economy," Mr Cameron is expected to say.
"Countries simply cannot continue to run indefinite structural fiscal deficits without contributing to the fundamental imbalances that fuelled the 2008 crisis."
His argument is likely to clash with that of new French president Francois Hollande, whose arrival on the global diplomatic stage has ruffled the feathers of those determined not to retreat on the need for austerity.
Mr Cameron will add: "The alternatives to action that create a more coherent eurozone are either perpetual stagnation from a eurozone crisis that is never resolved or a breakup caused by a failure to address underlying economic fundamentals that would have financial consequences that would damage the world economy – including Britain".
That approach was rejected by Labour leader Ed Miliband, who accused Mr Cameron of being "part of the problem, not the solution".
"All he offers is austerity which isn't working: austerity which has caused a double dip recession here in Britain, austerity which is not working internationally either," he said.
"If I was prime minister, I would be going to the G20 meeting of international leaders and arguing for a decisive shift towards jobs and growth."
He warned that Mr Cameron was in danger of "complacency" after the Greek election results. Negotiations are now underway in Athens as New Democracy leader Antonis Samaras seeks the formation of a 'national coalition'.
The prime minister's speech identifies five threats to the world economy, with the eurozone crisis and sovereign debt at the top of his list.
"Dealing with the first is vital to securing the second," Mr Cameron will say.
"Countries simply cannot continue to run indefinite structural fiscal deficits without contributing to the fundamental imbalances that fuelled the 2008 crisis in the first place."
He will also call for monetary activism and structural reform to deliver growth, as well as political commitment to avoid protectionist measures and follow through with moves to reform regulation of the international financial system.
"These five threats are very real, and let's be clear, in a global economy they threaten us all," the prime minister will say.
"We need to be absolutely clear about this and send an unequivocal message that deficit reduction and growth are not alternatives."
Leaders at the Los Cabos summit are not expected to emerge from the G20 summit tomorrow with a significant plan to address the world economy's problems.
But US president Barack Obama is expected to push for some form of action to be taken as improved prospects for the global economy would give his re-election campaign a significant boost.