"Let me be very clear, I'm not a Muslim leader or Muslims' spokesperson, I'm the mayor of London. I speak for all Londoners," the 45-year-old told reporters at a media briefing at his City Hall office on Wednesday.
Khan, however, said that his election proved "that it is possible to be Muslim and a Westerner. Western values are compatible with Islam".
The Labour party politician, who won an overwhelming mandate from Londoners last week and has been described as one of the most powerful Muslim politicians in Europe, repeated his criticism of presumptive US Republican presidential nominee Donald Trump, who has proposed banning all Muslims from entering the US but offered to make him an exception.
Khan, the son of a Pakistani bus driver, said Trump was "playing into the hands of the extremists".
The Labour party politician also repeated his support for Britain to stay in the European Union in the June 23 referendum.
"It's crucial for London to remain in the EU...Half a million jobs are directly dependant on the union," he said.