David Cameron said that "some good progress" had been made by EU leaders at an emergency summit towards agreeing a package of measure to resolve Europe's debt crisis.
The Prime Minister joined the other 26 EU leaders for urgent talks in Brussels amid mounting concerns about Europe's economic prospects - with German Chancellor Angela Merkel branding it the continent's worst crisis since the Second World War.
Emerging from the meeting - which will be followed by talks between countries who use the single currency - Mr Cameron said particular progress had been made on moves to recapitalise banks which had "not been watered down" and was now agreed as part of a three-pronged strategy.
"We have made some good progress tonight," he said.
Bank recapitalisation would only go ahead when all parts of the plan were agreed, he said, telling eurozone leaders: "Further progress on that needs to happen tonight."
Summit conclusions from the 27-leader meeting confirmed approval of the first of three key accords - strengthening the liquidity of the most exposed banks in Europe.
The recapitalisation of Europe's vulnerable banks - none in the UK - involves increasing their reserves by more than 100 billion euros (£87 billion).
The extra is supposed to be raised via private investors, but if that is not possible the top-up may have to come from the EU's bailout fund - basically from eurozone governments using taxpayers' cash once more.
The problem with the recapitalisation figure is that experts are already estimating that it is not enough. They say half as much again will be required to shore up banks sufficiently to satisfy markets.
The deal on recapitalisation remains subject to final agreement on the other two parts of the economic package being thrashed out - a much bigger bailout fund for the eurozone and a writing-off.