UPDATE 1-Greek ruling party support falls slightly--poll

* Support for government remains strong

* Popularity of PM Papandreou falls to 53 pct

* Most Greeks believe their economy will worsen

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ATHENS, May 16 (Reuters) - Greece's ruling Socialist party would get 45 percent of the vote if elections were held immediately, an opinion poll published in Kathimerini newspaper on Sunday showed, down from 46.5 percent in April.

The opposition conservative party would get 27 percent of the vote, down from 30 percent in April, according to the poll.

The austerity package Greece imposed in return for a 110 billion euro ($140 billion) EU and IMF bailout had little effect on support for the government.

But the popularity of Prime Minister George Papandreou, who is struggling to pull the country out of a debt crisis that has shaken the euro, fell to 53 percent, from 68 percent in April.

Greeks grew more pessimistic about their economy, with 61 percent saying they thought the economic situation would worsen, up from 50 percent in April's survey.

Markets are closely watching public reaction to the wage cuts and tax rises imposed by the Socialist government, and waiting to see whether the authorities will stand up to public pressure or water down the painful reforms.

Some 12,000 Communist Party supporters marched through central Athens on Saturday waving red flags and chanting slogans condemning the government.

Another poll, issued on Saturday, showed support for the ruling party fell to 28.6 percent in May from 34.5 in March. [ID: nLDE64E0AB] (Reporting by Angeliki Koutantou, editing by Tim Pearce)