Polish prosecutors have opened a terrorism investigation after a 24-year-old man opened fire in a busy market square in Kraków, killing six people including a Briton and injuring 17, in an attack that authorities said was probably inspired by far-right ideologies.

Police confirmed on Sunday that three people found dead at the gunman’s home after the attack on Saturday afternoon were his father, 53, mother, 52, and sister, 21.

As two days of national mourning began, the national prosecutor’s office said on social media it had launched an investigation into “the killing of six people … using a firearm, and the attempted murder of many others, including police officers, this act constituting a terrorist offence”.

The rare mass shooting has shocked a country that was considered safer than many of its western European neighbours, and has deepened concern after several school stabbings in October that left one woman dead and which officials said were linked to extremist content online.

The Kraków suspect, a Polish national, drove into the city’s main square in the heart of the old town, which is usually packed with tourists, at top speed at about 3pm on Saturday. Wearing military-style fatigues and a bulletproof vest, he started shooting at random as he took what the Kraków police spokesperson Katarzyna Cisło described as a “wild ride” around the square.

The interior minister, Marcin Kierwiński, said the suspect, who was apprehended and taken to hospital after being wounded in an exchange of fire with police, was fascinated with far-right ideologies and held “very radical” and “ultra-nationalistic” views.

Four women and two men were killed, including a British citizen, Polish police said. Three of the victims were Polish women and the remaining two have not yet been identified. Five of the wounded are foreign nationals from Britain, Austria, Germany, Portugal and Russia.

Two police ⁠officers were also among the injured, one of whom is in a serious condition. The suspect underwent surgery in hospital, where he is under heavy police guard.

The bodies of the suspect’s parents and sister were found at the family home in Ostrowiec Świętokrzyski, a town about 100 miles north-east of Kraków. Police said they had probably died of gunshot wounds.

Mourners have left candles in tribute to victims in the square, which was still partially cordoned off on Sunday. Flags across the country have been lowered to half mast, as have European flags outside the European Commission in Brussels “in solidarity with the Polish people”, the commission said.

The Polish defense minister, Władysław Kosiniak-Kamysz, called the shooting an “act of terror” on the people of Kraków, Poland’s second largest city, which receives 15 million visitors a year, most of them passing through the main square.

Kraków authorities said the square and adjoining streets “as well as sections along the perpetrator’s escape route will be closed for several hours”. Police in Warsaw, the Polish capital, said security had been bolstered there.

Maria, a 20-year-old employee at a cafe in Warsaw, told Reuters she “almost burst into tears” when she heard about the attack in Kraków. “Recent events – not just this one, but things happening lately – are really affecting our sense of security,” ⁠she said.

The daily newspaper Rzeczpospolita said in an editorial that the mass shooting had brought a “brutal end ​to an era in which Poland was ​considered an island of safety”.

The UK prime minister, Andy Burnham, said: “I’m shocked and saddened by the appalling shooting in Kraków today,. My thoughts are with the families of those who have lost their lives, everyone injured and all those affected by this senseless violence.”

The Ukrainian president, Volodymyr Zelenskyy, said his country stood in solidarity with its neighbour, calling the shooting a shocking crime.

France’s Emmanuel Macron described “shock and disbelief following the tragic shooting in Kraków”, while the German chancellor, Friedrich Merz, said: “The events in Kraków have deeply affected me,” adding that Germany stood with Poland “as a friend and partner in these difficult times”.

Italy’s prime minister, Giorgia Meloni, expressed condolences to Poland “following the vile and unacceptable act of violence”.