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Mr Fico was shot as he greeted crowds in front of a cultural community centre in the town of Handlova, where a government meeting had been held, reports say.
Several shots were heard, before his security detail bundled him into a nearby car. The Slovak leader has been taken to hospital and his alleged assailant detained by police.
Handlova is around 180km (112 miles) north-east of the capital Bratislava. A witness told the Dennik N website that she heard three or four shots and saw Mr Fico fall to the ground. She saw wounds to his head and chest.
Two of the prime minister’s guards quickly helped him and rushed him into a car. Local reports say he was then airlifted by helicopter to a nearby hospital.
A video showed several civilian bystanders as well as guards detaining the suspect just outside the cultural centre in Handlova. The BBC has not yet verified the footage.
In her initial reaction to the shooting, Slovakia’s outgoing president Zuzana Caputova said she was shocked by the “brutal and ruthless” attack on the prime minister and wished him strength to recover.
Mr Fico returned to power in Slovakia after elections last September, at the head of a populist-nationalist coalition.
His first few months as prime minister have proved highly contentious politically. In January he halted military aid to Ukraine and last month pushed through plans to abolish public broadcaster RTVS.