* Euro undermined by signs of early elections in Italy
* ECB chief Draghi points to need for continued stimulus
* Greece nerves also weighing
* Sterling weighed down by tightening polls
* Graphic: World FX rates in 2017 tmsnrt.rs/2egbfVh
By Patrick Graham
LONDON, May 30 (Reuters) - A new round of political worries over Greece, Italy and Britain had European currencies on the retreat against the dollar on Tuesday, the resulting bleaker mood on stock markets also pushing the yen broadly higher.
The dollar index, under pressure over the past fortnight from concerns over the Trump administration's difficulties, gained around 0.2 percent in early trade in Europe.
Low inflation readings out of Spain and one German region, as well as European Central Bank chief Mario Draghi's commitment to continued emergency stimulus in a speech on Monday, helped push the euro a quarter percent lower to $1.1135.
At the heart of the moves, however, were signs that elections in Italy may now come as early as September.
"We always knew Italy was going to come back into the market's sights but I think people thought we would have a longer stay of execution," said Rabobank currency strategist Jane Foley.
"It does seem like the market will have to face worries about elections and populism again over the summer. That of course is a drag for the euro."
Italian banks and blue chip shares fell sharply for a second day as U.S. and UK investors returned to their desks after Monday's holiday.
Other major markets were also deeply in the red, with French shares sinking 1 percent, prodding investors towards the traditional security of the yen. The Japanese currency gained around 0.3 percent against the dollar and 0.6 percent against the euro in morning trade in Europe.
After some relief while London was out on Monday, sterling is also back under pressure, teetering on the edge of a fall below $1.28.
Sterling bulls have been unnerved by the shrinking of Prime Minister Theresa May's lead in some polls to as low as 5-6 percentage points, suggesting the landslide she targetted a month ago may now be out of reach.
Analysts worry that will weaken her ability to face down hard line Brexiteers in her Conservative Party. But the prospect of a Labour Party-led government is also creeping onto the agenda.
A left-leaning administration led by Jeremy Corbyn might worry the debt market by borrowing and spending more on public finances, but it could also spell a softer approach to Britain's planned divorce with Europe.
"The main reason for the falls is that (with a smaller majority) there would be more political infighting. Maybe May would have to listen to the more extreme views on Brexit," said Commerzbank strategist Thu Lan Nguyen.
"If there really was a good chance that Labour was going to win, I think this could turn around. At this point does Labour have a smarter Brexit plan? I'm not entirely sure. But at least it would be a softer Brexit."
After recovering some ground on Monday, sterling was just 0.1 percent weaker at $1.2831 by 0740 GMT, up from Friday's three-week low of $1.2775.
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)