A gunman suspected of killing six people in central Krakow, and his parents and sister at their home, died in hospital early on Monday, Polish police have said.

The 24-year-old, who has been named as Michal Oksinski by local media, was injured after opening fire in central Krakow, the second largest city in Poland, on Saturday, police said.

Armed officers raced to the scene and engaged in a gunfight with the suspect, who was shot within three minutes of the attack beginning, preventing a further massacre, officials said.

Officials initially reported the gunman had apparently been inspired by "far-right ideologies", but have since said they are still investigating any possible motivation.

After the shooting, which began shortly before 15:00 local time (14:00 GMT) in Krakow's busy Main Market Square, police identified the attacker as a 24-year-old Polish man.

In the hours after the shooting, a minister said early investigations indicate he was inspired by "far-right ideologies". The minister also described him as an "ultra-nationalist" without giving further details.

However, during a press briefing on Monday morning, Przemysław Nowak, a spokesperson for Poland's National Prosecutor's Office, said investigations into his motive remain ongoing.

Six people - four women and two men - are confirmed to have been killed in the attack.

Four victims are Polish, while a British national and an Austrian woman were also killed.

Poland's Prime Minister Donald Tusk said three bodies - two women and one man - were found at the gunman's house when it was searched after the attack.

On Sunday, Polish police confirmed those three victims had been identified as the alleged gunman's 53-year-old father, 52-year-old mother and 21-year-old sister.

Polish media has reported the suspect had a firearms permit and may have obtained the weapons from his family home.

Four firearms were found in the gunman's car, including two AR-15 rifles and two handguns, along with several hundred rounds of ammunition, Nowak said. Authorities also seized at least four phones from his car and person, and electronic equipment from his home.

Sixteen people, including five foreigners, two police officers and the attacker, were taken to hospital. The interior ministry later said they were from Austria, Britain, Germany, Portugal and Russia.

Speaking on Sunday, one of two surgeons who treated victims on the street after the attack said his colleague "undoubtedly" saved the life of a gravely injured police officer.

The two surgeons, who were eating near the Main Market Square when the gunman opened fire, rushed to the scene to treat both the attacker and the two injured police officers.

Professor Michal Pędziwiatr told the BBC: "We saw the shooting attack. And what a surgeon can do in a situation like this?... We decided to help the victims as soon as possible."

"We rushed into the area where the shooting was and started our rescue, because there were no ambulances available, there were no professionals around."

Pędziwiatr said his colleague, who has been named by local media as Dr Mateusz Wierdak, used his hand to stem the bleeding from the most severely injured policeman, allowing time for an ambulance to arrive.

On Sunday it was reported that both injured officers had emerged from comas.

Witnesses who were near the Main Market Square have described their panic and confusion as the attack unfolded.

Ruby, from London, heard gunfire and "yelled at my friends to run and we all sprinted for our lives".

She said they "just kept sprinting" until they found a hotel to shelter inside.

Tom Brook, from West Yorkshire, was inside a McDonald's near the square when he heard "multiple gunshots and saw people running for cover".

"I then walked into the square and saw paramedics working on someone outside [a shop] and there was a dead body covered in foil blankets 20 meters away," he said.