LONDON (Reuters) - Today has brought fresh signs that the war in Iraq is shaking the fragile world economy even as the prospects of an early end to the conflict rise as U.S. troops approach Baghdad.

Reuters polls indicated that the services sector on which modern economies depend for much of their dynamism slowed sharply last month in both the euro zone and Britain, while Germany announced unemployment jumped to a five-year high last month.

A poll out later on Thursday in the United States is expected to show that its services sector has also become less buoyant.

European stocks rose again and world oil prices fell as traders monitored the situation in Iraq, where the United States said its troops had advanced to within 10 km (six miles) of the capital.

But with military experts predicting several more weeks of fighting, the signs of the possible economic fall-out were worrying their economic counterparts.

The Reuters eurozone services purchasing managers' index for March fell further below the 50 level that divides growth from shrinkage to 47.7 from 48.9 in February.

Data for the survey was collected from over 2,000 companies between March 14 and 27, with 65 percent of replies from the biggest economies -- France, Germany and Italy -- received before war began on March 20.

"Frankly, the data is terrible," said Alan Wilde, director of fixed income at Abbey National Asset Managers in Glasgow, Scotland.

"Maybe the mitigating factor is that people have written it off given events in Iraq...But on the face of it, the data is not helpful to a climate of economic recovery in the euro zone."

The survey followed one issued on Tuesday which showed manufacturing industry was also shrinking in the euro zone, after the index stuck its head above the magic 50 level in February.

BRITAIN TOO

A parallel services sector survey in Britain showed that it shrank last month for the first time since December 2001 with the index of business activity covering everything from restaurants to software consulting at 49.0 in March.

The Chartered Institute of Purchasing and Supply, whose February survey had given a reading of 50.2, blamed the fall on continuing uncertainty about the short to medium term outlook.

"Uncertainty had been further heightened by the build up to, and subsequent start of war in Iraq," it commented.

While the news was grave across Europe, it was particularly so in Germany.

The German purchasing managers' index hit a six-year low at 43.3, down from 43.6 in February, and the jobless figures showed 4.414 million Germans were out of work, the highest figure since February 1998.

The figure, adjusted for seasonal factors, was up 52,000 from February in the euro zone's biggest economy which has been struggling to achieve growth, economists say, because of outdated labour rules and generous social benefits. Joblessness now stands at 10.6 percent.

"In view of the stagnating economy and the Iraq war, no real upturn in the labour market can be expected before 2004," said Labour Office chief Florian Gerster.

ECB MEETING

German politicians have called for an easier monetary policy from the European Central Bank to spur their economy and those of their euro zone partners.

But they could hardly have been counting on the bank's council to emerge from a meeting in Athens on Thursday bearing such gifts.

With the progress of the Iraq war still uncertain, the ECB kept its key interest rate at 2.50 percent when it announced the outcome of its meeting at 1145 GMT.

The U.S. Federal Reserve is seen more likely to cut rates soon, and its decision could be influenced by the release at 1500 GMT of the March non-manufacturing index from the Institute for Supply Management.

Economists expect the index, the rough equivalent to the euro zone services PMI, to slip to 52.3 from 53.9 in February.

Meanwhile in Asia, governments trying to steer their economies through a global downturn exaggerated by the war in Iraq have an additional scourge to contend with -- disease.

But a meeting of Southeast Asian trade ministers in Laos on Thursday said they saw the economic impact of the flu-like Severe Acute Respiratory Syndrome as short-term.

The disease which originated in southern China and has now killed 80 people, most of them in Asia, could however impact one key sector of the continent's economy, they admitted.

"I think we only worry about tourism," Thai Commerce Minister Adisai Bodharamik told Reuters, wearing a mask to protect himself against infection as he passed through Bangkok international airport on the way to the get-together.