Tomas Taraba told the BBC Mr Fico's surgery had gone "well" and "I guess that at the end he will survive".
Earlier the defence minister said Mr Fico was "fighting for his life" after being gravely injured in an attack in the small town of Handlova.
A suspect was detained at the scene of the shooting.
Interior Minister Matus Sutaj Estoka described it as a politically motivated assassination attempt.
Following the shooting, Mr Fico was rushed to hospital and spent several hours in surgery "fighting for his life", according to Defence Minister Robert Kalinak, who spoke at a news conference from outside the hospital where Mr Fico was being treated on Wednesday.
There has been no official update on the prime minister's condition since then, but his second-in-command has since told the BBC's Newshour programme that Mr Fico was "not in [a] life-threatening situation at this moment".
"As far as I know, the operation went well and I guess that at the end he will survive," Mr Taraba said.
Mr Taraba added that the prime minister was shot "from very close" and that "one bullet went through the stomach and the second one hit the joint".
Police have not yet identified the alleged suspect. Unconfirmed local media reports say he was a 71-year-old writer and political activist.
AzVision.az
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