LONDON  - Euro zone money markets started to fully price in a December interest rate cut from the European Central Bank on Wednesday, as the spread of coronavirus outside of China pushed traders to ramp up expectations for more stimulus.

Eonia money market futures dated to the ECB's December 10 meeting now show about 10 basis points of rate cuts being priced in, up from around 7.5 bps on Monday ECBWATCH . That equates to around a full probability of a 10 bps cut from the bank.

The probability of an ECB rate cut in July also rose significantly, to around 70% from 50% on Monday.

Europe's worst flare up yet of the virus in Italy has raised fears that its contracting economy could soon be thrown into another recession.

Asia reported hundreds of new coronavirus cases on Wednesday, including the first U.S. soldier to be infected, as the United States warned of an inevitable pandemic.

Expectations for a rate cut have risen across money markets in recent weeks as analysts try to gauge the extent of the economic impact the coronavirus could have and the support needed to mitigate it.

Traders are now pricing in more than two rate cuts from the Federal Reserve by the end of the year FEDWATCH and a cut from the Bank of England by September BOEWATCH .

"The first thing to say is that, to put it quite bluntly, the ECB is not going to cure anyone from the disease. You can even have doubts about how rate cuts would help in economic growth," said ING senior rates strategist Antoine Bouvet.

He was citing a debate on how effective negative rates are in supporting the region's sluggish economy.

ECB policymaker Francois Villeroy de Galhau said on Tuesday that there was currently no need for more monetary policy action in the face of the coronavirus outbreak. 

"Nevertheless the market needs to price some reaction, and the ECB is the only game in town," ING's Bouvet added.

Expectations for meaningful fiscal stimulus remain low as repeated attempts to boost investment and growth have failed in countries led by Germany.

Most 10-year euro zone bond yields were flat, with Germany's benchmark at a 4-1/2 month low of -0.52%. 

Italian bonds, which have born the brunt of a sell-off in lower-rated, southern European debt this week, remained under pressure, with the 10-year yield rising 5 bps in early trade. It touched a one-month high at 1.04%. 

In the primary market, Germany is scheduled to sell 4 billion euros of five-year bonds.

(Reporting by Yoruk Bahceli; editing by Marc Jones) ((Yoruk.Bahceli@thomsonreuters.com; +44 20 7542 7571; Reuters Messaging: yoruk.bahceli@thomsonreuters.com))