LONDON (Reuters) - Concern over Italy’s banks and Britain’s national election dominated holiday-thinned European financial markets on Monday, pushing stock markets lower after Asian share indices fell back off two-year highs.

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Sterling, hammered by a slump for Prime Minister Theresa May’s Conservatives in opinion polls last week, recovered after weekend polls confirmed the trend but showed her still on course to win next week’s vote.

European share prices were lower [.EU] overall, but Italian banks and blue chips fell as worries over recapitalisations of regional Italian lenders bled over into a second week.

Weekend reports that Italy’s main parties could converge on a proportional electoral law pointed to growing chances of an early election that may yield an indecisive hung parliament.

“The risk of early elections has suddenly increased to 60 percent,” LC Macro Advisers founder Lorenzo Codogno said. “A hung parliament is thus the most likely outcome.”

European blue chips .STOXXE overall slipped 0.2 percent, but losses for Banco BPM BAMI.MI, Unicredit CRDI.MI and others drove a 3.4 percent loss for Italy's banking index - its biggest in nearly four months .FTIT8300.

Milan's main blue-chip index fell almost 2 percent .FTMIB while Germany's DAX .GDAXI was little changed.

Asian markets were also lower overall after some early gains that largely shrugged off another missile launch by North Korea, the broad MSCI index of Asia-Pacific shares outside Japan .MIAPJ0000PUS dipping 0.2 percent.

Japan's Nikkei .N225 edged up 0.2 percent while Australian shares .AXJO fell as much as 0.8 percent, hit by another round of falls in the prices of oil and other commodities. China's markets are also closed on Monday and Tuesday for a holiday.

On currency markets, the dollar was flat, trading at $1.1185 per euro and 111.35 yen after steadying on a better batch of U.S. economic data on Friday that solidified expectations of a rise in official interest rates next month.

San Francisco Federal Reserve President John Williams said in Singapore on Monday that medium-term trends in U.S. inflation remained “pretty favourable,” despite some recent soft consumer price data.

After falling more than 2 cents last week, sterling was 0.2 to 0.3 percent stronger against the dollar GBP= and euro EURGBP=.

“A lot of what we are seeing is the after effects of Friday’s news and data releases,” said Thu Lan Nguyen, a currency strategist with Commerzbank in Frankfurt.

“We have a little bit of dollar strength following better U.S. data and some hawkish comments from Federal Reserve officials. And we have a little bit of a pound recovery following the latest poll results from the UK.”

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(This version of the story has been refiled to restore missing phrase from first paragraph)