Authorities have said it is "not surprising" two stabbings have taken place in the space of a week in the city
Police have responded to serious incidents in Cowley Road in Littlemore on Sunday and in Edgecombe Road in Barton on Thursday night.
Tobias Bruce, 33, died in hospital as a result of the first stabbing as police investigate the two incidents.
A man has sustained several stab wounds and was taken to hospital following the Barton incident, where he remains in a serious condition at this time.
One man, aged 26 and from Barton, has been arrested on suspicion of section 18 wounding with intent and obstructing or resisting a constable.
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Bayswater Road in Barton was closed in both directions throughout Friday as police carried out investigations.
Thames Valley Police said it is "keeping an open mind" with regards to a connection between the two.
A spokesman for Thames Valley Police said: "At present, we do not believe the incidents to be linked, although naturally, we are keeping an open mind with regards to this while our investigation continues."
Police and crime commissioner for the Thames Valley, Matthew Barber, said such incidents were always "tragically sad" but that he wanted a "much tougher" approach to knife possession.
Mr Barber added: "It is not acceptable from a police perspective.
"We will be increasing patrols in hotspot areas and using stop and search appropriately.
"We are also looking at funding a number of initiatives.
"If we don't intervene early it could end up potentially ruining lives."
Local policing commander for Oxford, Superintendent Bruce Riddell, said there will be an increased police presence in both Littlemore and Barton over the weekend.
City councillor Jabu Nala-Hartley, who lives in Edgecombe Road, suggested increased stop and search might not always be effective.
The Barton and Sandhills ward representative said: "Searching people randomly is a downstream rather than upstream model.
"It's not a long-term solution in terms of looking for the root causes as to why young people are engaging in this destructive behaviour."
Labour councillor Mike Rowley, who also represents the Barton and Sandhills ward, said: "Obviously my thoughts are with the victim first and foremost.
"Certainly I'm not surprised by it.
"I am concerned about cuts to community policing in Oxford.
"I do think that having community police who local people trust is very important."
Local policing commander for Oxford, superintendent Bruce Riddell, said: “I understand that the recent news of two incidents in Oxford involving knives will undoubtedly have caused concern amongst the local community.
“Firstly, my thoughts are with the victim’s family and friends at this difficult time.
“It is important to stress that at present, we do not believe the incidents to be linked, although naturally, we will keep an open mind while our investigation continues.
“I would like to reassure you that we take robust action against those found to be carrying and using knives in Oxford and we will investigate thoroughly to seek to prosecute those involved."
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