European shares fell on Thursday, with banks among the biggest fallers on worries that some of them will have to follow UniCredit's lead and offer deep discounts in share prices when they recapitalise.

Italy's UniCredit fell 17.3 percent, adding to a 14.5 percent fall on Wednesday, when it announced a massive discount on a rights issue. The STOXX Europe 600 euro zone Banking Index <.SX7E> fell 5.7 percent, while Italy's FTSE MIB index <.FTMIB> was down 3.7 percent.

The FTSEurofirst 300 <.FTEU3> index of top European shares fell 0.8 percent to a provisional close of 1,013.38 points, having hit a five-month high on Tuesday.

The fall came despite upbeat jobs data. U.S. private-sector hiring surged in December as employers added 325,000 new workers while claims for jobless benefits fell, raising hope that recent labour market improvement would continue in 2012.

You'd think the UniCredit thing would have been priced in by now, though the market has been looking a touch overbought, said Mike Lenhoff, chief strategist and head of research at Brewin Dolphin Securities, in London.

Hopefully the (U.S. labour) figures aren't a fluke and will be endorsed by a decent set of non-farm payrolls tomorrow. If we get that the markets will pick up and go.

(Reporting by Brian Gorman)