David Cameron has urged fellow EU leaders to take "decisive" action over Greece and agree longer-term plans to beat the wider eurozone crisis.
Arriving for an EU summit over dinner in Brussels the Prime Minister said: "This is an important meeting for Britain because what happens in the eurozone affects our country."
It was time for decisive plans for Greece, to help get the economy moving, he said, adding: "But if we are not to keep coming back and back to meetings like this we also need coherent long term plans - otherwise this crisis will keep re-occurring."
New French President Francois Hollande arrived for his first EU gathering of leaders since his election insisting on the need for more emphasis on economic growth - setting himself up for a major showdown with German Chancellor Angela Merkel, who says austerity measures must take priority to tackle debt and deficits.
He also pressed the case for establishing eurobonds in the 17-nation eurozone to raise money to take the pressure off indebted countries - anathema to Germany, which would see the cost of its borrowing rise.
The summit opened amid falling markets as speculation rose about eurozone readiness to concede that Greek departure from the single currency may be inevitable.
In London the FTSE 100 Index closed 2.5% lower, off 136.9 points at 5266.4.
EU officials say little can be done - or said - by EU leaders to resolve the Greek crisis until a national election re-run due on 17 June.
Meanwhile, they said, the focus is on restoring confidence in the European economy through a series of practical measures to inject more growth into the current austerity-based remedies being imposed on Greece in return for massive financial bail-outs.
The only clear agreement at the summit was determination to keep Greece in the eurozone if possible.
But officially Greece was not on the dinner debate menu, where the agenda centres on growth-boosting initiatives, such as targeting more money on major structural projects to generate jobs and revenue and reinforcing the EU's single market for trade.
None of the ideas are new and Mr Cameron insisted: "If we're not going to keep coming back and back to meetings like this, we need to deal with some of the longer term issues at the heart of running a single currency - having a bank that gets behind that single currency; having coherent long term plans to make sure that single currency is coherent. We have to address those issues too or these crises will keep re occurring."
The plight of Greece will be discussed later tonight: "We will discuss Greece after the dinner, but of course there is a crucial election yet to come in Greece and our scope is limited: we don't want to look as if we are interfering in that election," said one official.
The fear is that a summit word out of place could worsen the crisis in Athens in the run-up to the sensitive poll on 17 June which could dictate the next step in the single currency saga.
On the eve of the talks Tory MEP Martin Callanan told the European Parliament: "So we are having yet another summit - the twenty-second in the last two and half years.
"None of the others have made any material difference, so why should this one?
"The reason all of these summits have failed is because none of them have addressed the real problem - the collapse in our competitiveness."
European business leaders, in a letter to the summit signed by BUSINESSEUROPE President Jurgen R. Thumann, said:
"The summit urgently needs to demonstrate to businesses, investors and citizens across our continent and beyond that it has a coherent and credible plan to resolve the present crisis and put Europe back on the path towards long-term sustainable growth."
A pre-summit accord on setting up "project bonds" to speed investments in transport, energy and information technology involves the EU setting aside 230 million euro (£184m) in guarantees to support the issuing of bonds for European infrastructure projects.
The relatively small sum could be "leveraged" to mobilise private investments of more than 4bn euro (£3.2 bn), say experts, sending a positive signal ahead of the crucial Greek election.