In the full count, Igor Dodon won 52.2 per cent of the vote. Maia Sandu, who ran on an anti-corruption ticket, had 47.8 per cent. Russian President Vladimir Putin invited Dodon to visit Moscow and said he looked forward to developing bilateral relations.
In her first comments after the final results, Sandu said the elections were neither free nor fair and accused opponents of using "dirty methods" including the media and administrative resources, against her.
International election observers said today "fundamental freedoms (were) respected, but polarised media coverage, harsh rhetoric detracted from the process."
Today, up to 3,000 mostly young Moldovans marched to the offices of the Central Election Committee in Chisinau shouting "Down with the Mafia!"
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Anger had also flared yesterday after Moldovans voting in Britain, Ireland, France, Italy and elsewhere lined up for hours and ballot papers ran out. Sandu said the elections had been badly organised.
Dodon's victory was celebrated with fireworks early Monday in the semi-autonomous Gagauzia region, home of many ethnic Russians.
Putin congratulated Dodon and said the outcome of the elections demonstrates Moldovans want to have a balanced foreign policy."
The statement said the Russian leader is willing to develop bilateral relations within an existing friendship agreement.
Romania's president, Klaus Iohannis, was cooler and more reserved in his remarks, saying the new president should fulfil his mandate "with wisdom and balance," and respect "the constitutional attributes" of the post.