* Poll shows leftist opposition ahead of ruling conservatives
* EU elections in May seen as test for PM Samaras's coalition
* Far-right Golden Dawn in third place, ties with new party (Adds protests, poll details)
ATHENS, March 20 (Reuters) - Greece's anti-austerity opposition held a two-point lead over the ruling conservatives in the latest opinion poll before European elections in May that are viewed as a test of support for Prime Minister Antonis Samaras's shaky coalition.
Polls so far had shown the two parties running neck-and-neck or with the opposition party Syriza slightly ahead.
The Pulse poll for the To Pontiki newspaper published on Thursday also showed that To Potami, a movement launched barely a month ago, had shot up to third place alongside the far-right Golden Dawn party.
Leftist Syriza, which opposes Greece's EU/IMF bailout and the tough conditions that come with it, would get 19 percent of the vote if EU elections were held now, two percentage points ahead of Samaras's New Democracy, the poll showed.
The Golden Dawn party, many of whose lawmakers are under criminal investigation following the killing of an anti-fascist rapper by a party sympathiser last September, remained the third most popular political force with 10 percent.
It tied with To Potami, a party launched by a popular TV journalist at the end of February that has won strong support from voters disgusted by the political establishment.
Greece's two bailouts since 2010, worth 240 billion euros, have come at the price of wage and pension cuts and tax rises. Thousands of businesses have closed during a six-year recession and unemployment has hit 27.5 percent, more than double the euro zone average.
Dozens of state high school teachers marched to parliament on Thursday on the second day of a 48-hour strike by public sector workers against planned layoffs, holding banners which read "No to firings!".
Earlier, about 30 people occupied an office belonging to the minister in charge of overhauling the public sector, Kyriakos Mitsotakis, in a symbolic protest.
The Pulse survey was carried out on March 17 and 18, as Athens wrapped up six months of wrangling with its international creditors to unblock the next tranche of rescue loans.
It put support for Syriza at 23 percent if national elections were held today, compared to 21.5 percent for New Democracy, narrowing its lead from three percentage points in a previous poll in January.
Greece is due to hold its next national elections in 2016. (Reporting by Karolina Tagaris; Editing by Raissa Kasolowsky)