The shooting was the first major assassination attempt on a European political leader for more than 20 years, and has drawn international condemnation.
Political analysts and MPs say it has exposed an increasingly febrile and polarised political climate both in Slovakia and across the continent.
"He is able to speak but only a few sentences and then he is really tired because he is on some medication," president-elect Peter Pellegrini, a Fico ally, told reporters after visiting the 59-year-old prime minister in hospital.
Earlier, Deputy Prime Minister Robert Kalinak said it was too early to say whether Fico would recover from the attack due to "the extent of the injuries caused by four gunshot wounds".
Slovak president-elect Peter Pellegrini has urged political parties to tone down their campaigning. (EPA PHOTO)
Interior Minister Matus Sutaj Estok, speaking at the same news conference, said the shooter - whom police have charged with attempted murder - had acted alone and had previously taken part in anti-government protests.
"This is a lone wolf who had radicalised himself in the latest period after the presidential election (in April)," Sutaj Estok said.
Slovak news media have said the shooter is a 71-year-old former security guard at a shopping mall and the author of three collections of poetry.
There has been no official confirmation of his identity.
The suspect listed government policies on Ukraine and its plans to reform the country's public broadcaster and dismantle the special prosecutor's office that deals with high-level corruption as reasons for the attack, Sutaj Estok said.
Police gave no details about their investigation at an afternoon news conference but said they had boosted security at Slovakia's parliament and also around media offices and schools.
Miriam Lapunikova, director of the FD Roosevelt University Hospital in Banska Bystrica where Fico is being treated, said he had undergone five hours of surgery with two teams to treat multiple gunshot wounds.
"At this point his condition is stabilised but is truly very serious. He will be in the intensive care unit," she told reporters.
Slovak President Zuzana Caputova called for a calming of political tensions.
Appearing alongside her at a news conference before visiting Fico, Pellegrini urged parties to suspend or tone down their campaigning for next month's European Parliament elections.
"If there is anything the people of Slovakia urgently need today, it is at least a basic consensus and unity among Slovaks' political representatives," said Pellegrini, winner of the hard-fought April election for the mainly ceremonial presidency.
Fico has dominated Slovak politics for much of the past two decades, winning re-election last October for a fourth stint as prime minister.
He has fused progressive economic views with nationalism, tapping into widespread discontent over living standards but has also proved a divisive figure.
His critics say new reforms threaten the rule of law and media freedoms in Slovakia, a member state of the European Union and NATO.
Fico's calls for ending sanctions on Russia and halting arms supplies to Ukraine have endeared him to the Kremlin, and President Vladimir Putin and other Russian politicians have been prominent among those condemning Wednesday's assassination attempt.
Fico was shot while greeting supporters in the street after chairing a government meeting in the central town of Handlova.
Neighbours of the suspect in the town of Levice, south of Handlova, expressed shock at the news, saying he had shown no sign of political extremism.
"He was a polite man and wasn't strong about politics as such but he did feel that some of the measures of the government weren't correct," pensioner Mile Ludovit, 68, told Reuters through an interpreter.
Fico and his government coalition allies have criticised sections of the media and the opposition, saying they had inflamed tensions in the central European country.
