After his second operation on Friday, there is cause for optimism, the Minister added.
However, Fico cannot yet be transferred to the capital, Bratislava, in the coming days, Defence Minister Robert Kalinak said.
A panel of doctors is to decide on Monday whether he is to be transferred.
The Prime Minister is currently recovering in the university hospital Banska Bystrica, close to the small town of Handlova where he was shot.
On Saturday, the gunman who attacked Fico was remanded in custody, following a decision by a special court responsible for organised and politically motivated crime in the western city of Pezinok, court spokeswoman Katarina Kudjakova told dpa.
She said this was due to the risk he might abscond and carry out further acts of violence.
The decision can be appealed.
The man was detained directly after the shooting on Wednesday. Reports, citing the police, said he had already pleaded guilty during questioning.
The public prosecutor's office asked for him to be held in pre-trial detention and the court heard Juraj C, as he is known under privacy rules, on Saturday morning.
He had been expecting Fico after a government meeting in Handlova and shot at him at close range.
Fico, 59, was hit by several gunshots and has since undergone two operations.
The suspect, 71, was charged on Thursday with attempted murder. He was described by authorities as a "lone wolf" motivated by political grievances.
The attack, on the deeply divided nation, sent shock waves around the world.
Since then, there has been an increase in threats against other politicians in the country, Interior Minister Matus Sutaj Estok told the daily newspaper Pravda on Saturday.
Since then, there has been an increase in threats against other politicians in the country, the Interior Minister told the daily newspaper Pravda on Saturday.
A member of Parliament from Smer, the largest governing party led by Fico, had also been threatened.
A perpetrator has been identified in both cases.
Earlier death threats against the liberal opposition leader Michal Simecka and his family had already been made public.
Apart from specific death threats, the number of aggressive comments on social media has also increased significantly, Slovakian media reported, citing experts.