One woman was killed and five other people were injured by a man with a knife in central London on Wednesday night.
"The safety of all Londoners is my number one priority and my heart goes out to the victims of the incident in Russell Square and their loved ones," Khan said in a statement today.
"I have spoken with the commissioner, and the assistant commissioner, who have assured me that our police officers are working extremely hard to investigate exactly what has happened and to keep the rest of us safe.
"A man was arrested at the scene. Police have spoken to him and are seeking to establish the full facts including motives for this attack."
The mayor continued: "I urge all Londoners to remain calm and vigilant. Please report anything suspicious to the police. We all have a vital role to play as eyes and ears for our police and security services and in helping to ensure London is protected.
"Our police officers are doing an incredibly difficult job on our behalf and they have my full support."