* European shares dip, Asian markets also off highs
* Sterling recovers some ground with London on holiday
* Speculation of early Italian election after weekend reports
* Italian banks down 2 percent
* Graphic: World FX rates in 2017 tmsnrt.rs/2egbfVh
By Patrick Graham and Danilo Masoni
LONDON, May 29 (Reuters) - Concerns over Italy's banks and Britain's national election campaign dominated holiday-thinned European financial markets on Monday, prodding stock markets lower after Asian share indices fell back off 2-year highs.
Sterling, hammered by a slump for Prime Minister Theresa May's Conservatives in opinion polls last week, recovered some ground after weekend numbers confirmed the trend but showed her still on course to win next week's vote.
European share prices were a touch lower, led by a half-percent fall in banking shares 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 also pointed to growing chances of an early election that carries the risk of a win for the anti-establishment 5-Star movement.
"If approved, the new law could significantly increase the chances of a vote in the autumn ... It remains to be seen what the chances of a stable parliamentary majority will be," one trader said.
European blue chips eased 0.2 percent, with Italy's Banco BPM and Unicredit both down around 2 percent. Germany's DAX was little changed.
Asian markets were 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 dipping 0.2 percent.
Japan's Nikkei edged up 0.2 percent while Australian shares 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.
South Korea's KOSPI added 0.4 percent to touch a record high and was on track for its seventh straight day of gains.
"There are not many negative factors in the market for the KOSPI, and demand seems still strong enough to push the index up a bit more," said Kim Ji-hyung, a stock analyst at Hanyang Securities.
On currency markets, the dollar was broadly flat, trading at $1.1180 per euro and 111.34 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 0.25 percent stronger against the dollar and euro.
"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."
For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.biz/cms/?pageId=livemarkets (Editing by Andrew Heavens)