A 16-year-old was found with stab wounds to the leg and was taken to hospital for treatment, after being arrested in connection with the incident.
He has now been charged with possession of a machete.
An 18-year-old man, who was also arrested, has been charged with possession of cocaine and heroin with intent to supply and possession of a machete.
Both were due to appear at court today.
In response to the incident, police boosted patrols and stop and search powers in a large area of Leeds to crack down on people carrying violent weapons.
Under Section 60 of the Criminal Justice and Public Order Act 1994, officers have the power to search people or vehicles for offensive weapons or dangerous instruments without them having to have their usual grounds to suspect each person searched.
The order was initially in place until 2pm today (Friday) and has now been extended for a further 24 hours - subject to review.
It covers the area bordering York Road, Harehills Lane, Claypit Lane, the A58, the A61 and Woodhouse Lane, as shown on the map provided.
There have been ten stop searches in the last 24 hours.
Police have made three arrests on suspicion of possessing offensive weapons - identified as machetes.
Superintendent Russ Hughes, of Leeds District, said: “After very careful consideration, we have assessed that there remains a clear need for continued use of Section 60 powers to support our work to target and deter those carrying weapons, with the aim of preventing any further serious violence.
“The feedback we are getting through our local neighbourhood policing teams is that people in the communities involved are widely supportive of our continued use of this tactic.
“We recognise the need for openness and accountability and are continuing to work closely with local community representatives to that end.
“The carrying of weapons and their use to commit serious violence is completely unacceptable and creates understandable concern in the community.
"We are determined to keep doing everything we can to disrupt, deter and bring to justice those who involve themselves in this type of criminal behaviour.”