Sadiq Khan tweeted and appeal for the public to help police with their investigations into the deaths, which are not thought to be connected.
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.
No one has been arrested.
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.
Three men and woman have been arrested on suspicion of murder and taken to separate south London police stations for questioning.
Neither victim has been formally identified.