Jeroen Dijsselbloem, the Dutch finance minister, is the latest senior politician to concede that Greece may yet need a third bailout, casting a shadow over news that eurozone companies are reporting their strongest growth for more than two years.

Dijsselbloem, who heads the eurogroup of finance ministers, told Dutch newspaper Het Financieele Dagblad: “The problems in Greece won’t be solved in 2014, so something more will have to happen.” He said the form and scale of another rescue would depend on Greece’s progress with economic reforms.

His admission echoed that of the German finance minister, Wolfgang Schäuble, who told an election campaign event earlier this week that the bailed-out country still needed more aid. The International Monetary Fund has suggested that there is an €11bn (£9.4bn) shortfall in the current rescue package for Greece.

The spectre of destabilising negotiations over a new bailout, though they are unlikely to get under way until after German elections next month, were a reminder that the eurozone is still not out of the woods, despite an upbeat survey suggesting economic recovery in the 17-member zone is gathering steam.

The monthly purchasing managers’ indices, which test the confidence of firms across the 17 member-states, showed both manufacturing and services expanding at their fastest pace since summer 2011.

Chris Williamson, chief economist at data provider Markit, which compiles the indices, said: “The euro area’s economic recovery gained momentum in August.”

Apolline Menut, of Barclays, said: “The readings confirm that recovery is on track and that GDP should continue to grow in the third quarter.”

However, while Germany scored a PMI reading of 53.4 – well above the 50 level which marks expansion, suggesting recovery in the eurozone’s largest economy is gathering speed – output in France declined, and at a faster pace than during July, according to the survey, with both manufacturing and services output falling. Williamson said: “A big question mark still hangs over France’s ability to return to sustained growth.”

Across the eurozone as a whole, export sales rose for the second month in a row, Markit said, and new orders for manufactured goods jumped at their fastest pace since May 2011.

However, some analysts remain more sceptical about whether the nascent upturn – after an 18 month recession – is set to last, particularly if the US Federal Reserve’s plan to “taper”, or start reducing, its $85bn a month quantitative easing programme continues to push up government bond yields on this side of the Atlantic, raising the cost of borrowing.

A research note from City consultancy Fathom said: “The fundamental structural problems facing the euro area have not gone away. In addition, the potential spillovers from Fed tapering pose a threat to debt sustainability in the periphery … we are a long way from calling an end to the euro area crisis.”

Investors were cheered by a similar survey of China’s manufacturing survey, published by HSBC, which suggested output may be stabilising, after growth deteriorated sharply at the start of the year. The reading on the purchasing managers’ index rose to a stronger-than-expected 50.1 for August, from 47.7 in July – the largest monthly jump in three years.

Analysts said there were hopeful signs that China is succeeding in shifting its growth model away from exports, towards consumer spending.

“Domestic demand is strong enough to support 7.5% [growth] in 2013,” said Ken Peng, senior economist at BNP Paribas in Beijing. “Almost all of China’s economic data since July has shown improvements and suggests a rebound is under way.”

Fears about a so-called hard landing in China have exacerbated recent jitters in financial markets over the fate of emerging economies when the Fed withdraws from QE.

Yields on US government bonds hit a fresh two-year high, as minutes from the Fed’s latest meeting, released on Wednesday night, confirmed that QE could start to be phased out as soon as next month.

However, the dollar’s relentless rise was briefly checked after a worse-than-expected labour market survey, which suggested new claims for unemployment benefits had risen by 13,000, to 336,000, in the past week.

“The Fed tapering theme continues. The minutes reinforced expectations that the Fed will taper its quantitative easing programme in September and Thursday’s jobless claims didn’t really change that,” said Greg Moore, currency strategist at TD Securities in Toronto.