(ADVISORY- Follow European and UK stock markets in real time on the Reuters Live Markets blog on Eikon - see cpurl://apps.cp./cms/?pageId=livemarkets) Adds details, closing prices)
* STOXX Europe 600 index little changed
* Italian banks bounce on ECB support hopes
* Miners, Oils lead sectoral fallers
* Actelion hits fresh record
By Danilo Masoni and Atul Prakash
MILAN/LONDON, Nov 29 (Reuters) - European shares rose slightly on Tuesday, helped by a strong rebound in Italian banks, while reports of a improved takeover offer sent Swiss biotech Actelion rallying to a fresh all-time high.
Italy's bank index rose 4.1 percent, helped by a Reuters report that the European Central Bank stands ready to buy more Italian bonds if a referendum on Prime Minister Matteo Renzi's constitutional reform this weekend rocks markets.
The pan-European STOXX 600 index ended up 0.3 percent with gains in the broader European banking sector more than offsetting losses among mining and energy stocks.
Italian lenders UBI, Intesa Sanpaolo and UniCredit rose between 3.1 and 5.8 percent, while troubled lender Monte dei Paschi surged 17.5 percent, erasing losses seen on Monday which were due to worries over its ability to execute a vital 5 billion euros capital raising.
The Italian banking index has fallen around 15 percent from its levels two weeks ago as investors reduced their exposure to the country's assets before the Dec. 4 referendum that could unseat Renzi. Renzi has said he would resign if the reform, as polls predict, is rejected.
"Looking at today's moves, it seems that some investors are considering the recent sell-off in Italian banks as overdone. It could be some last minute portfolio adjustments ahead of the referendum," Peter Dixon, economist at Commerzbank, said.
"All those uncertainties related to the Italian referendum still exist. We will take a very cautious view on the country's banking sector."
The chief executive of the Italian stock exchange said that big international investors were holding huge short positions on Italian assets.
Later in the day, sentiment was boosted after Reuters reported the ECB was ready temporarily to step up purchases of Italian government bonds if the result of Sunday's referendum sharply drives up the country's borrowing costs. Italian banks have a big sovereign debt exposure.
Actelion ended up 10 percent, reversing earlier losses after reports said U.S. healthcare company Johnson & Johnson is raising its offer for Swiss group in an attempt to win it over for a buyout.
The European basic resources index fell 1.4 percent, the top sectoral decliner, as prices for lead and zinc fell more than 6 percent from the previous day's multi-year peaks, as sliding oil prices and perceptions that a post-U.S. election rally had become overstretched prompted selling. Mining companies Antofagasta, BHP Billiton, and Fresnillo were the biggest fallers, down by between 3 and 3.9 percent.
The oil and gas index fell 0.9 percent, as oil prices fell almost 4 percent on signs leading oil exporters in OPEC were struggling to agree on a deal to cut production to reduce global oversupply. BP was the biggest weight to the index, falling 2.1 percent.
TalkTalk rose 3.1 percent, rebounding off 4-year lows, after Britain's telecoms regulator said it would go to the European Commission to try to force BT to legally separate from Openreach, the network that delivers broadband to millions of homes and businesses.
Openreach is the division of BT Group that develops and maintains the UK's main telecoms network used by telecom providers such as Sky, TalkTalk, Vodafone and BT's retail business. (Reporting by Danilo Masoni)