LONDON, Dec 4 (Reuters) - Euro zone government bond yields dropped to multi-month lows on Monday as market bets on interest rate cuts ramped up following comments from European and U.S. policymakers last week.

Greece's 10-year yield fell to its lowest since June after Fitch upgraded the country's sovereign rating to investment grade, following a similar move by S&P Global in October.

Bloomberg quoted European Central Bank rate setter Francois Villeroy de Galhau at a conference on Friday, saying that barring any shock, rate hikes were now over, adding that the central bank may consider cutting interest rates next year as the process of disinflation had been "faster than expected".

Euro zone inflation eased to 2.4% in November from 2.9% in October, data showed last week, prompting bets that the ECB will begin cutting interest rates sooner than previously thought.

ECB euro short-term rate (ESTR) forwards price in around 130 basis points of rate cuts by the end of next year , from around 90 basis points at the start of last week.

Markets are also pricing in around an 75% chance that the ECB will begin cutting interest rates in March , from around a 40% chance a week ago.

"Central banks are coming down from rate hikes and that risk is being priced out," said Anders Svendsen, chief analyst at Nordea.

"If you think there's a very low risk of rate hikes, then you need to position for lower rates," Svendsen added.

Germany's 10-year yield, the euro area's benchmark, was last down around half a basis point at 2.357%, having dropped to 2.349% earlier, its lowest since July 19.

Germany's policy-sensitive 2-year yield was 2.5 basis points higher at 2.687% but earlier dropped to 2.659%, its lowest since May 16. On Friday, it fell more than 15 basis points in its biggest one-day drop since March's banking turmoil.

Policymakers have tried to pour cold water on easing expectations with ECB Vice-President Luis De Guindos and German rate setter Joachim Nagel both saying it was too early to declare victory over inflation.

Markets are also pricing in rate cuts from the Federal Reserve early next year even as Chair Jerome Powell on Friday said the central bank was prepared to tighten policy further if appropriate.

Powell added that the risks of slowing the economy more than necessary have become "more balanced", reaffirming the central bank's intent to be cautious but also offering fresh optimism on progress so far.

"Even though Powell tried to keep rate hikes on the table, I don't think he was very convincing. The markets didn't buy it," said Nordea's Svendsen.

Greek bonds outperformed after Fitch's move, with the ratings agency citing the sharp downward trend in general government debt.

Fitch raised Greece's sovereign rating to 'BBB-' from 'BB+' with a stable outlook, making Greece's bonds eligible for a wide range of bond indexes that require investment grade ratings from multiple agencies.

Its 10-year government bond yield dropped as much as 7 basis points to 3.573%, its lowest level since June 27.

"This paves the way for Greece to rejoin the major sovereign bond indices in January," said Commerzbank rates strategist Rainer Guntermann in a note.

"However, most of the support should be in the price by now."

Italy's 10-year yield, the benchmark for the euro zone's periphery, rose half a basis point to 4.109%, pushing the spread between the German and Italian 10-year yields to 174 basis points. (Reporting by Samuel Indyk; Editing by Kirsten Donovan)