The victim remains in a critical but stable condition after being airlifted to hospital with a stab wound to his lower back.
Detectives have not yet made an arrest, but say the man is believed to have been attacked by "several men" in Grafton Street, off Fishergate Hill at around 3.30pm.
DI Chris Wellard, who is leading the investigation, says he believes the men were known to each other and the stabbing was a targeted attack.
Yesterday, he said: "At this time we are treating this as a targeted attack and believe there is no wider threat to the public.
"However, this was a serious attack on someone who has been left with critical injuries and we will have extra patrols in the area for reassurance and anybody with concerns is welcome to speak to an officer.”
Today (Monday, June 7), the force has renewed its appeal for those who might have witnessed the attack to come forward with information.
A police spokesman said: "Enquiries are ongoing and we continue to appeal to anyone in the area at the time who saw the group or has any information, to come forward."
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