* Support for ruling conservatives edges higher - poll
* Parliament to vote Sunday on controversial reform package
* Athens needs to pass law to obtain further bailout funds (Recasts with opinion poll, adds Prime Minister)
By Angeliki Koutantou and Harry Papachristou
ATHENS, March 29 (Reuters) - The main party in Greece's ruling coalition, conservative New Democracy, has nudged ahead of the leftist opposition for the first time in six months, an opinion poll showed on Saturday, ahead of a key parliamentary vote on more tough reforms.
The poll will be welcome news for Prime Minister Antonis Samaras' fragile government, whose cohesion has been tested by the controversial reforms demanded by international lenders as a condition to keep debt-laden Greece afloat.
The poll, conducted on March 24-27 by Alco for weekly newspaper Proto Thema, showed Samaras' New Democracy winning 21.7 percent of the vote if elections were held today, against 21.2 percent for the main opposition, anti-bailout Syriza party.
In Alco's previous poll on March 11-13, Syriza led New Democracy by 21.2 to 20 percent, a lead similar to that in all other polls tracked by Reuters in recent months.
Alco's is the first major poll conducted since Samaras promised this month to spend a 527 million-euro windfall out of Greece's 2013 budget surplus on poor, austerity-hit Greeks, saying this was a first sign of the country gradually exiting the painful budget cuts imposed by lenders.
The spending package is wrapped in a 225-page reform law to be voted late on Sunday. The law has caused friction within the government for removing protectionist measures shielding several professions such as milk producers, publishers and pharmacists.
Deputy Agriculture Minister Maximos Charakopoulos resigned his post on Saturday to protest against the draft law, saying it would hurt farmers by encouraging imports of cheap foreign milk.
However, Charakopoulos suggested he would not vote against the bill to avoid derailing the country's bailout.
"At this point, my political ethics do not allow me to put the country's smooth financing at risk," he said in a statement.
REDUCED MAJORITY
New Democracy and its coalition partner, the Socialist PASOK party, have 153 lawmakers in the 300-seat parliament. Two pro-government lawmakers have threatened to vote against the law. But Samaras may be able to pass it with as few as 148 votes because six lawmakers of the far-right Golden Dawn party are in jail awaiting trial and cannot take part in votes.
The law includes all new reform measures Athens agreed earlier this month with the European Union and the International Monetary Fund after more than six months of tough negotiations.
Greece must pass the law to qualify for further bailout funds and repay 9.3 billion euros of debt maturing in May.
Eurozone finance ministers are scheduled to review Greece's reform progress when they meet in Athens on Tuesday. Samaras expects lenders to disburse the funds and then start talks soon on how to provide further debt relief for Greece, which last year outperformed the fiscal goals set by its lenders.
"We have kept our promises, so our lenders will keep theirs," he was quoted as saying on Saturday in an interview with newspaper Realnews. "I believe that the (debt relief) issue will be settled by the fall," he added.
The draft bill allows Greece's bank bailout fund HFSF more flexibility and legal cover to sell bank stakes it holds to private investors. Syriza leader Alexis Tsipras threatened on Friday to sue government officials who will use provisions of the law to sell its bank stakes.
The bill also includes anti-corruption clauses, including 15,000-150,000 euro fines on prime ministers, cabinet ministers and lawmakers caught red-handed.
Greek labour unions have called rallies outside parliament on Sunday to protest against the draft law. Pharmacists have been on strike since Wednesday and seamen said they would walk off the job on Monday and Tuesday. (Additional reporting by Renee Maltezou; Editing by Gareth Jones)
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