"We cannot imagine this could stop somehow," Fico, the head of a centre-left coalition cabinet, said in a moderated discussion with his Czech counterpart on the public Czech Television channel.
"It is theoretically possible, but I really can't imagine British politicians standing up against the outcome of the referendum," he added.
In the chaotic wake of Britain's shock June 23 vote to leave the European Union there has been speculation about whether the country's leaders could effectively annul the referendum's results.
MPs in the 150-member Slovak parliament started petitioning for a similar referendum in Slovakia.
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It needs to collect 350,000 signatures for the referendum to be held.
In the neighbouring Czech Republic, which formed a single country with Slovakia until 1993, President Milos Zeman said Thursday he would "do his best to have a referendum" on the Czech Republic's exit from the EU and NATO.
But Czech Prime Minister Bohuslav Sobotka said in the debate with Fico that his centre-left government "would not hold a referendum on leaving the EU or NATO.