(REUTERS) -- The pace of decline in the Eurozone private sector eased unexpectedly in December, but the global toll of the region's sovereign debt crisis became clearer on Thursday with news of falling investment and factory activity in China.

While a recession has almost certainly started in the Eurozone, Markit's flash composite purchasing managers' index (PMI), which corresponds closely with economic growth, raised some hope it might not be as deep as first feared.

(It) reinforces the notion that the Eurozone economy is slipping into a mild recession rather than falling off a cliff, said Martin van Vliet, senior economist at ING.

Even so, the survey compilers warned against viewing its latest gauge of Eurozone business as a turning point, especially since there is still a strong risk the Eurozone sovereign debt crisis could spiral out of control.

EU leaders last week took a historic step towards fiscal union last week, but pressure is building on reluctant Eurozone paymaster Germany to take immediate, radical steps to solve the crisis.

Indeed, there is growing evidence the debt crisis has already damaged the global economy, impeding the fervent growth of emerging economies like China that are so dependent on European export markets.

China saw its first year-on-year drop in foreign direct investment in 28 months in November, while PMIs there showed factory activity slowed for a second month.

The U.S. has perhaps been the only major economy that has enjoyed a run of good news recently, which could extend into a glut of jobs and industry data due at 1330 GMT.

EURO PERIPHERY STILL STRUGGLES

Most economists gave a cautious welcome to the Eurozone PMI data, which measures changes in the activities of thousands of businesses across the Eurozone.

All in all, despite the further pick-up in December, the PMI data still suggest that Eurozone real GDP saw a marked contraction in the fourth quarter, said ING's van Vliet.

The Markit Eurozone Composite PMI, which looks at both the manufacturing and services sectors, rose unexpectedly in December to 47.9 from 47.0 last month.

But it has now lingered below the 50 line that divides growth from contraction for four months.

Furthermore, only France and Germany were responsible for the upturn in the index, while the Eurozone's peripheral economies continued to struggle.

Markit said its data pointed to a quarterly economic decline of 0.6 percent in the Eurozone in the final quarter of this year.

That would be twice as deep as the contraction expected by economists in a Reuters poll on Wednesday, which also forecast a 0.2 percent fall in the first three months of the new year.

An escalation of the debt crisis could cause a far steeper contraction next year -- a scenario the Swiss National Bank warned on Thursday could not be ruled out, after holding its exchange rate cap on the franc against the euro for now.

There was one bright note on Thursday. The risk premium on benchmark Spanish bonds fell following a well-received bond auction that raised more than the government had targeted.

CHINESE CHILLS

Fresh signs that China's economic growth is slowing emerged on Thursday with the first year-on-year drop in foreign direct investment (FDI) in 28 months, while a fresh fall in new orders signaled a further contraction in factory activity.

November's $8.8 billion of commitments were down 9.8 percent on November 2010, the first fall since July 2009's 35.7 percent year-on-year collapse to $5.4 billion.

A sharp drop in inflows from the U.S. was a particular drag, slowing year-to-date growth in FDI flows to 13.2 percent from 15.9 percent in October's data.

The overall trade environment next year for China will be complicated, partly due to the economic uncertainties in the European countries, and I should say that the export situation in the first quarter of next year will be very severe, Commerce Ministry spokesman Shen Danyang told a news conference at the release of the FDI data.

The European Union is China's largest export partner, meaning the debt crisis has had a harsh impact on China's vast manufacturing economy.

The HSBC flash manufacturing purchasing managers' index, the earliest indicator of China's industrial activity, rose modestly to 49.0 in December from 47.7 but pointing to a monthly contraction in activity nonetheless.

With inflation quickly shifting to disinflation, the Chinese government can and should make more aggressive easing on both fiscal and monetary fronts to stabilize growth and jobs, said Qu Hongbin, chief China economist at HSBC.

(Additional reporting by Aileen Wang and Koh Gui Qing in Beijing, Editing by Ross Finley and Hugh Lawson)