Khan is likely to travel to US by the end of the year to discuss about the threat proposed by Trump over banning the entry of Muslims in the US.
Speaking to reporters, Khan said he had successfully beaten the Conservatives' Donald Trump approach to elections. "I think what we've shown' and I hope it's a lesson that Hillary and others in America take on board; hope does 'trump' fear, forgive the pun," he said.
Meanwhile, Trump had said in an interview to the The New York Times that he was happy to see Khan take over his new post and that "there will always be exceptions" to his controversial Muslim ban comments.
Responding to Trump's 'exception' remarks, Khan said: "This isn't just about me. It's about my friends, my family and everyone who comes from a background similar to mine, anywhere in the world."
Khan officially took charge as the London Mayor on Saturday, May 7 following the election, which saw him defeat his Conservative rival Zac Goldsmith by 1,310,143 votes to 994,614.