Syriza, which opposes the EU-IMF bailout deal, initially grabbed an early lead yesterday in both the city of Athens and the greater region, exit polls showed.
But as the results began coming in, the incumbent Athens mayor and governor, who are backed by the socialist Pasok party in the government coalition, narrowed the gap.
Nevertheless, the radical leftist party's 39-year-old leader Alexis Tsipras insisted his movement could still deal a fatal blow in the second round on May 25.
Syriza want to use these local elections -- and the European polls next week -- as a referendum against austerity and springboard for general elections, which could come as early as February next year.
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Prime Minister Antonis Samaras, head of the conservative New Democracy party, had warned that a vote for Syriza could derail reforms demanded by the country's EU-IMF creditors.
"This is a battle in which Greece must show that it has the stability that it deserves," the prime minister told reporters.
With nearly 30 per cent of polling stations accounted for, government candidates seemed set to hold on to the city of Thessaloniki and the key regions of Thessaly, the Peloponnese and Crete.
But the government could lose the main port of Piraeus, where the conservative mayor is lagging behind a candidate openly backed by the city's favourite sports club, Olympiakos.