The Mayor of London tweeted he was “sickened” after the attacks, which are not thought to be connected.
Sadiq Khan appealed for the public to help police with their investigations into the deaths.
At 4:42pm on Friday, police were called to Deeside Road in Wandsworth, following reports of a stabbing.
Officers and paramedics attended and found a man, believed to be in his late teens, in critical condition.
He died at the scene shortly afterwards.
Six men have been arrested on suspicion of murder and taken to separate west London police stations for questioning.
Just 12 minutes later at 4:54pm, officers were called to a car park in Hartville Road in Plumstead, southeast London, to reports of a shooting.
A man, who is believed to be a teenager, was found critically injured. He died at the scene a short while later.
Four people, three men and a woman, have been arrested.
Neither victim has been formally identified.
Police recorded 732 homicides in England and Wales last year, the highest total in a decade, according to official figures released in April. Meanwhile, the number of offences involving knives or sharp instruments increased by 6% in 2018 compared to the previous 12 months.
The figures came after a spate of knife crimes involving young people sparked a political row over cuts to police funding.
Research given exclusively to Sky News last month revealed knife crime and gang culture has left a quarter of young people feeling unsafe where they live.