* FTSEurofirst 300 up 2.3 pct, Euro STOXX 50 up 2.8 pct

* Biggest daily gains in 10 wks follow steep Friday fall

* Heavily-shorted Nokia gains on Lumia demand hopes

By Toni Vorobyova

LONDON, Nov 19 (Reuters) - European equities rebounded from multi-month lows on Monday to post their biggest daily gain in 10 weeks thanks to signs of progress in U.S. talks to avoid a budget crisis.

Leading Democratic and Republican lawmakers voiced confidence over the weekend that a deal would be reached to avoid the so-called "fiscal cliff" of some $600 billion of tax hikes and spending cuts which threatens to plunge the United States into recession in 2013.

An unexpected rise in U.S. existing home sales for October added to the brighter sentiment towards the world's biggest economy on Monday, which has become a significant source of growth for European companies as their domestic region stagnates.

"The news about the fiscal cliff over the past few days has been much more positive," said Donald Huber, portfolio manager at Franklin Templeton Investments, which has about $750 billion in assets under management.

"I don't think it's going to be an easy process overall, but there are a number of possible solutions shaping up, so my guess is that they're going to work through it."

The FTSEurofirst 300 index provisionally closed up 2.3 percent to 1,091.50 points, while the EuroSTOXX 50 rose 2.8 percent to 2,495.19 points -- both posting their biggest one-day gain since early September and rebounding from multi-month lows.

The rebound comes after EuroSTOXX 50 dipped into technically oversold territory on the 7-day relative strength index (RSI) on Friday for the first time in nearly two months.

Then, a big rally followed but ran out of steam after two sessions, and this time too analysts were doubtful about the sustainability of the gains unless the fiscal cliff problem is actually resolved rather than just postponed.

"We had the lows and the market is oversold ... so it is just short-covering," said Vincent Guenzi, chief strategist at Cholet Dupont.

"That (progress in negotiations) was the catalyst for the short term gain of the market. That could help the market may be gain 1 or 2 percent more, but to really have the end of the downtrend of the last weeks we need something real."

Monday's broad-based rally took all the STOXX 600 sector indexes into positive territory, led by economically-sensitive ones like autos, banks, construction, technology and basic resources.

Healthcare, which is less dependent on economic cycles for demand, lagged with a rise of 1.0 percent.

Nokia was a top gainer among individual stocks, with reports of its Lumia 920 selling out in Germany fuelling hopes of strong demand for the new smartphone.

Shares in the Finnish cellphone maker added 9 percent on Monday, but are still down 39 percent since the start of 2012.

Nokia is the most shorted company in EuroSTOXX 50, with 19.7 percent of outstanding shares on loan according to data from Markit, potentially making it vulnerable to sharp short-covering rallies on any sentiment improvement or positive news.

That gives Nokia a utilisation rate - shares borrowed versus the total number available for loan - of 93.5 percent, against just 6.2 percent for EuroSTOXX 50 as a whole.