Miners push European shares down for second day; Italian banks mixed

(Corrects day in first paragraph)

* Pan-European STOXX 600 index down 1.6 percent

* Mining stocks index leads sectoral fallers in Europe

* Monte Paschi hits new all-time low, GS upgrade boosts UniCredit (EUREX: DE000A163206.EX - news)

* UK housebuilders drop after poor industry data

* HSBC sees more outflows from European equities

By Danilo Masoni

MILAN, July 5 (Reuters) - European shares fell on Tuesday, weighed down by losses among mining stocks, while the Italian bank Monte dei Paschi (Milan: BMPS.MI - news) plunged to a fresh record low on continued worries about its capital strength.

The pan-European STOXX 600 index was down 1.6 percent by 0838 GMT, adding to losses seen on Monday, while the FTSEurofirst 300 declined by 1.5 percent.

European stocks rose last week as expectations grew that European central banks would step in to support markets spooked by Britain's vote to leave the European Union.

But both indexes remain below levels reached before the UK vote, which triggered worries about the political and economic outlook for Europe, weighing particularly on peripheral countries such as Italy and financial stocks.

"All problems are still in front of us after the Brexit vote... and investors will remain cautious before the earnings season starts in a few days," said Jerome Schupp, head of research at SYZ Asset Management in Geneva.

As Brexit concerns continue to linger, HSBC equity strategist Robert Parkes said outflows from European equities were likely to continue after hitting their highest level on record in the first half of the year.

Monte dei Paschi fell 7 percent, making it the biggest faller on the STOXX 600 index, after Italian newspapers said the government was in talks with the European Commission about injecting capital into the bank without imposing losses on retail investors.

The European Central Bank has asked Italy's third-largest lender to slash its bad debt by 40 percent in three years, heightening concerns that the bank may have to launch a cash call at a time when investor appetite for bank stocks is low.

"Banks in Europe are a big concern for different reasons, from low interest rates to volatile markets. For Italian banks, it will take years to digest bad loans," Schupp said.

Europe's bank sector index, the worst sectoral performer this year, and since the Brexit vote, was down 1.7 percent, although some Italian lenders turned positive after heavy falls in the previous session.

UniCredit rose 2.3 percent after Goldman Sachs (NYSE: GS-PB - news) upgraded it to "buy" from "neutral" even though the U.S (Other OTC: UBGXF - news) . broker said it was at high risk of contagion in the event smaller lenders failing.

UK housebuilders fell after data showed Britain's construction industry suffered its worst contraction in seven years in June as concerns over the Brexit vote intensified. Shares (Berlin: DI6.BE - news) in Barratt Development, Taylor Wimpey (LSE: TW.L - news) and Berkeley Group were down between 4.8 and 6.2 percent.

Europe's STOXX 600 Basic Resources index, which contains major mining stocks, topped sectoral fallers with a decline of around 3.7 percent, as copper prices eased from a two-month peak on concerns over Chinese demand. (Reporting by Danilo Masoni; Editing by Kevin Liffey)