Opinion polls showed the political parties aiming for membership in the European Union were roughly neck-and-neck with those that back joining Russia in a customs union.
Russia and the EU are locked in a tug-of-war to win influence in the region where armed conflict has erupted in neighbouring Ukraine between Kiev's pro-EU leadership and pro-Russian separatists.
Moscow does not want to part ways with Moldova, a former Soviet satellite where it has troops stationed in the Russian-speaking breakaway region of Transdniestr, while the EU is keen for Moldova to be a success story for its soft power.
A small country of 3.6 million wedged between Ukraine and EU member Romania, around 78 per cent of Moldova's population is ethnic Romanian, while Ukrainians and Russians account for around 14 per cent.
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One of Europe's poorest countries, Moldova has struggled to break free from persistent political crisis.
In June Chisinau signed an historic association accord with the European Union in the face of bitter Russian opposition. It gained visa-free travel for its citizens and access to a free trade zone as well as hundreds of millions of euros in funding.
Moldova is currently run by a pro-European coalition headed by Prime Minister Iurie Leanca that wants more integration with Europe.
The presidents of Poland, Ukraine and Romania visited Moldova last week to back the pro-EU campaign, while German Chancellor Angela Merkel sent a message of support to Leanca.