The gunman shot Fico, 59, five times, initially leaving the prime minister in critical condition and undergoing surgery hours later on Wednesday evening.
"I was very shocked ... fortunately as far as I know the operation went well - and I guess in the end he will survive ... he's not in a life-threatening situation at this moment," Slovak Deputy Prime Minister and Environment Minister Tomas Taraba told the BBC's Newshour.
Taraba said one bullet went through Fico's stomach and a second hit a joint.
News outlet Aktuality.sk cited an unnamed source saying Fico was out of surgery and in stable condition.
Defence Minister Robert Kalinak told a news briefing hours earlier that Fico had suffered "serious polytrauma" after several shot wounds.
Interior Minister Matus Sutaj Estok had said earlier that Fico was in a life-threatening condition while he remained in the operating room.
"This assassination (attempt) was politically motivated and the perpetrator's decision was born closely after the presidential election," Sutaj Estok said, referring to an April election won by a Fico ally, Peter Pellegrini.
The shooting in the central Slovak town of Handlova, which Slovak media said was carried out by a 71-year-old man, stunned the small central European nation and drew international condemnation.
Slovakia, a member of NATO and the European Union, has little history of political violence. Russian President Vladimir Putin and U.S. President Joe Biden joined Slovakia's EU partners in expressing shock and condemnation of the shooting.
The country of 5.4 million has seen polarised political debate in recent years, including the hard-fought presidential election last month that helped tighten Fico's grip on power.
Since returning as prime minister last October, Fico has shifted policy quickly. Opposition critics call it a power grab.
His government has scaled back support for Ukraine while opening dialogue with Russia, sought to weaken punishments for corruption and dismantled a special prosecutor's office, and is revamping the RTVS public broadcaster despite calls to protect media freedom.
Fico has long been critical of Slovakia's mainstream media, refusing to speak to some outlets. Members of his party blasted media and opposition actions in recent months.
"I ask all to stop piling attacks, expressions of hate, on social networks, in the media, which are aimed at that or another political camp, regardless if it concerns the (government) coalition or the opposition," Sutaj Estok said.
After the attack, Fico was rushed to hospital in Handlova where he had been chairing a government meeting. He was then transported by helicopter to regional capital Banska Bystrica for urgent treatment, it said, adding that his condition was too serious for him to be taken to Bratislava.
A Reuters witness heard shots as Fico exited a building to shake hands with a crowd of people who had been waiting to greet him. Police then wrestled a man to the ground.
Slovak news media reported the shooter was a former security guard at a shopping mall, an author of three collections of poetry and a member of the Slovak Society of Writers. News outlet Aktuality.sk cited his son as saying his father was the legal holder of a gun licence.
"I have absolutely no idea what my father intended, what he planned, what happened," it quoted the son as saying.
Broadcaster TA3 reported the leftist prime minister had been hit in the abdomen in the attack.
"I don't think I will wake up from this," 66-year-old Lubica Valkova told reporters on the scene. "This kind of thing just can't happen in Slovakia."
VETERAN LEADER
Fico, a dominant force in Slovakia for two decades, has drawn criticism for taking a more pro-Russian stance in the Ukraine war.
Describing the shooting as a "monstrous" crime, Putin said in a telegram sent to Slovakia's President Zuzana Caputova: "I know Robert Fico as a courageous and strong-minded man. I very much hope that these qualities will help him to survive this difficult situation."
Biden offered U.S. help to Slovakia, saying in a statement: "We condemn this horrific act of violence."
Slovakia's biggest opposition party Progressive Slovakia called off a planned protest and called for restraint to avoid escalating tensions. Parliament suspended debate indefinitelyafter the attack.
In his career, Fico has moved between the pro-European mainstream and nationalistic positions opposed to EU and U.S. policies. He has also shown a willingness to change course depending on public opinion or changed political realities.
An admirer of Hungary's Prime Minister Viktor Orban, Fico has grown increasingly critical of Western support for Ukraine in its war with invading Russian forces.
Fico was forced to resign as premier amid mass protests in 2018 triggered by the contract killing of Jan Kuciak, a journalist who had been investigating high-level corruption. Those protests exacerbated divisions in Slovak society that still linger.
