Rashan Charles, 20, was seen trying to swallow an object in a shop in Hackney, early on Saturday morning.
Protesters are planning a vigil outside an east London police station on Monday evening after his death.
The vigil organised by Hackney Stand Up to Racism and Fascism, which said on their Facebook page that they are "enormously concerned and angered" over Charles' death.
London pastor and chairman of the Peace Alliance Rev Nims Obunge told Premier: "We just need to pray for communities at a time like this that there is calm and we don't have anything like what we've had in years-past like something like a riot or anything that is excessive.
"We just need to pray that in the midst of the pain and in the midst of the anguish that communities feel - people from certain communities may feel we just have to pray. Ask Church members and ask Christians for peace in our city."
According to the Metropolitan Police, an officer pursued Mr Charles on foot after attempting to stop a car in Kingsland Road at 1.45am.
The force said that after entering a shop he was seen "trying to swallow an object" and was then taken ill.
Mr Charles died in hospital around an hour later.
Footage apparently showing the incident leading to his death has been posted on social media with the hashtag #JusticeForRash.
The vigil's organisers added: "Only weeks after the death of Edson De Costa in Newham after he was arrested by police, this latest incident continues the seemingly endless list of young black men dying at the hands of the authorities."
Chief Superintendent Simon Laurence, borough commander for Hackney, urged people to keep up-to-date with information from the Independent Police Complaints Commission (IPCC).
He said: "The Independent Police Complaints Commission has launched an independent investigation to establish what happened and has viewed the officers' body worn video.
"There is likely to be speculation over the next few days regarding what led to this man becoming ill, so I would encourage people to keep up-to-date with the IPCC's statements, as and when they are released.
"All police officers are fully aware that they will be asked to account for their actions - officers are not exempt from the law and we would not wish to be."
Rev Nims Obunge said it's vital the police give reassurance to communities.
He explained: "Whatever happens in relation to the protest today - [it is important] that young people still feel that justice will be served if needed in a situation like this."
There is currently no evidence to suggest racism was a factor in the death of Shashan Charles.
IPCC investigators are keen to speak to any witnesses who were in the Kingsland Road/Middleton Road area of Hackney at the time.
It said it had obtained evidence "which indicates an object was removed from his throat at the scene".
The vigil is scheduled to begin tonight at 6pm outside Stoke Newington police station.