A man who was stabbed to death in the early hours of Sunday after a row in a shop in East Dulwich, south-east London, has been identified.

The Metropolitan police said on Monday evening that while they were still awaiting formal identification, the force was confident the victim was Dennis Anderson, 39, from Lewisham, south-east London.

The Met appealed for information about the killing, which was one of a string of violent incidents to take place in the capital at the weekend.

Reports had suggested Anderson was attacked when an argument broke out after he refused to give a man cigarettes.

On Monday, DI Domenica Catino from Scotland Yard’s homicide and major crime command said: “We are aware of speculation around the motive for this attack and can now confirm that the suspect approached Mr Anderson in an off-licence shop before an altercation broke out and the suspect delivered a fatal attack.

“Our top priorities now are to support Mr Anderson’s family and catch the person responsible for this horrible attack. Officers are working around the clock to locate this suspect and bring him into custody.”

There were two stabbings in the capital on Saturday. Last year, there were 128 homicides in London, the highest number in a calendar year this decade. Scotland Yard’s murder investigation unit has lost 25% of its officers and staff over a decade.

Earlier on Monday, it was announced that knife crime offenders in London will be tagged with tracking devices upon their release from prison in an attempt to reduce violence.

Those who have served custodial sentences for knife-related crimes such as possession, robbery, wounding, grievous bodily harm and aggravated burglary will be subject to the tagging under a year-long pilot scheme.

The programme, beginning on 18 February, will be used on up to 100 offenders deemed likely to reoffend in four London boroughs that have among the highest rates of knife crime – Lewisham, Lambeth, Croydon and Southwark.

The tags will automatically check the movements of the offenders against the location of reported crimes, and share significant matches with the police.

The London mayor, Sadiq Khan, said: “The causes of violent crime are extremely complex and involve deep-seated problems – such as poverty, inequality, social alienation and a lack of opportunities for young people – that enforcement alone won’t solve and have been made much worse by huge government cuts to the police and preventative services.

“This innovative pilot will build on the good work of the City Hall-funded violent crime taskforce by helping offenders integrate back into society and reducing the risk of reoffending, as well as giving the police the information they need to thoroughly investigate reported crimes.”

Carina Heckroodt, the head of the London extremism, gangs and organised crime unit in the National Probation Service, said: “These tags will provide a constant physical reminder of an offender’s licence conditions, encouraging them to comply with their restrictions and deterring them from further offending, and protecting victims.”

On Saturday evening, a 23-year-old man was left in a critical condition after he was stabbed in Neasden, north-west London. A 29-year-old man was arrested at the scene on suspicion of attempted murder, and a 24-year-old woman was detained on suspicion of assisting an offender.

At about 4pm on the same day in Hayes, west London, four people – one aged 15, one 16 and two 18 – were arrested after a 16-year-old boy was found with a stab wound when police responded to reports of a fight.