European share indexes have ended flat after a week of volatile trading.

The main indexes in the UK, France and Germany rose slightly on Friday, but over the week the FTSE fell 3.6%, the Cac 40 shed 4.4% and the Dax lost 4%.

The volatility prompted the G20 to put out a statement late on Thursday reassuring that it was ready to take action to stabilise markets.

IMF chief Christine Lagarde said the challenge the world faced "could not be more urgent".

"There are dark clouds over Europe and there is huge uncertainty in the US," she said in an address to the annual meeting of the World Bank and the IMF in Washington.

"And with that we could risk a collapse in global demand.

"We are all in it together and nobody should be under any illusion that there could be a de-coupling."

Capitalisation problem

Global shares had slumped on Thursday, sparked by a Federal Reserve warning late the previous day about the outlook for the US economy.

Gloomy comments about weak global growth from the International Monetary Fund (IMF) and the World Bank knocked sentiment further.

On Thursday, IMF head Christine Lagarde said the global economic situation was entering a "dangerous place", while World Bank president Robert Zoellick said he thought the world was in a "danger zone".

Doubts about the strength of European banks also resurfaced on Friday, after the head of France's markets regulator, Jean-Pierre Jouyet, said "there is indeed a problem with the capitalisation of banks".

He said 15 to 20 banks needed additional funds, none of which were based in France.

Image caption John Frary was approaching retirement and faced a tough financial choice That money had just gone in two or three weeks due to a very sharp downturn in a very short period of time John Frary from Bedfordshire has seen his retirement fund fall by £7,000 in value in four weeks Pensions and Isas hit by turmoil

Meanwhile, Greece has denied media reports it was contemplating defaulting on its debts, with creditors taking a 50% hit on Greek government bonds.

Finance Minister Evangelos Venizelos said Athens was focusing on reducing its debt levels.

"All other discussions, rumours, comments and scenarios which are diverting our attention from this central target and Greece's political obligation... do not help our common European task," he said.

On Friday, credit rating agency Moody's downgraded eight Greek banks due to concerns about Greece's ability to pay back its debts.

Two of the Greek banks downgraded, the Emporiki Bank of Greece and General Bank of Greece, are majority-owned by France's Credit Agricole and Societe Generale respectively.

'Bold action'

The IMF and World Bank comments, following the Fed's warning about "serious downside risks" to the US economy, helped to push global markets sharply lower on Thursday, with the main European indexes falling about 5%, and the Dow Jones on Wall Street closing down 3.5%.

Overnight, Asian shares fell sharply, with South Korea's main Kospi index slumping 5.7% and Hong Kong's Hang Seng losing 1.4%. Japan's Nikkei was closed for a public holiday.

The European and US falls sparked the G20 to announce a commitment "to take all necessary actions to preserve the stability of banking systems and financial markets as required".

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It said it would follow up this pledge with a "bold action plan" at the beginning of November.

Analysts said investors were unimpressed by the announcement.

"The statement from the G20 last night may have taken the edge off the current bitter market sentiment, but the reassurances from the finance ministers lack substance," said Jane Foley at Rabobank.

"Until politicians back their actions with words in respect to moving closer to a solution to the eurozone debt crisis, markets will continue to worry about a messy and painful outcome from the eurozone debt crisis."

The G20 has given little hint of what action it may take, but markets have long been calling for a substantial increase in the eurozone's communal bailout fund, the European Financial Stability Facility (EFSF), from its agreed level of 440bn euros ($596bn; £385bn).

Many investors also want the eurozone to issue bonds guaranteed by every one of the 17-member nations - so-called eurobonds. However, a number of policymakers, particularly those in Germany, have resisted the idea.

In July, European finance ministers proposed making the EFSF more flexible, allowing it to buy individual government bonds - which would bring down the cost of borrowing for heavily indebted nations - and to offer emergency credit lines to banks. However, the proposals have not yet been ratified.

'Drip feed'

Analysts say far swifter action is needed in order to soothe investors' jittery nerves.

"Markets work on a second by second basis, while politicians seem to be working to a monthly calendar," Jeremy Stretch from CIBC told the BBC.

He highlighted the "drip feed effect" of this week's IMF downgrade of global growth, the Fed's warning, the further comments from both the IMF and World Bank and Thursday's weak figures on eurozone private sector growth as undermining investors' confidence even further.

Gerard Lyons at Standard Chartered Bank also highlighted political inertia, telling the BBC: "My biggest worry is that there is not the sense of urgency that there really needs to be to force policymakers to take decisive action".

The G20 is gathering later in Washington, a meeting which Jim O'Neill, chairman of Goldman Sachs Asset Management, suggested could mark the beginning of concerted action to tackle the debt crisis in Europe which is the cause of so much stock market volatility.

"The thing that really brought the world to a better place in 2008 was genuine collective action involving both the developed and the developing world through the G20," he told the BBC.

"The fact that they're all there together in [Washington] DC this weekend should lay the framework for thoughts about quite significant actions... sometime between now or possibly at the November G20 in France."