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 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.

People mourn on Sunday near the…