The 24-year-old was attacked on a Glasgow street during a row with three other people yesterday morning.
Police Scotland said the motive for the assault is not yet clear, but they believe it would have been witnessed by motorists and passers-by.
The incident happened at around 10.30am on Balmore Road, where there was a row involving the victim, two other men and a woman.
The 24-year-old was stabbed by one of the men in the attack, which is thought to have taken place opposite a bus stop near Balmore Square.
Emergency services took the injured man to the Glasgow Royal Infirmary, where medical staff describe his condition as serious but stable.
After the attack, the other three people made their way up Balmore Road toward the Lambhill area, police said.
The suspect and the woman made their way along the street on the right hand side of the road and the other man walked along the left hand side of the road.
The incident is being treated as a murder bid by police, who want anyone with information to get in touch.
The suspect is described as white, in his early 20s, around 5ft 8ins, of medium build and with short dark hair. He was wearing a grey hooded tracksuit top with a black t-shirt underneath, grey jogging bottoms and white trainers.
The other man is said to be white, of a similar age and around 5ft 8ins. He was wearing an orange hooded top with dark jeans and black trainers.
The woman is described as being white, in her early 20s, with a thin petite build.
Officers said they have been carrying out door-to-door inquiries and are collecting CCTV images from the area.
Detective Sergeant Alan Cuthbert said: "It's not clear what the motive was for this particular attack. We know that there was an altercation between them which left the 24-year-old man with serious stab wounds.
"The assault occurred on the roadway mid-morning and I'm sure it would have been witnessed by passers-by and motorists. There are also a number of business premises and we are keen to hear from owners and staff. If you have any knowledge or information about the incident or the suspect, please do get in touch."
CID officers at Maryhill Police Office can be contacted on the police non-emergency number 101.