Keith Kerr, a contender for the Liberal Democrat nomination, urged Mr Phillips to abandon his campaign, saying the black journalist and broadcaster should "back down to preserve his dignity".
Launching his own campaign, Mr Kerr, British Airways' customer service manager, said Ken Livingstone was the choice of Labour Party members.
Mr Kerr, who claims to be "one of the most senior black corporate executives in any of the FTSE 100 companies", told Mr Phillips: "If you are allowed to run against Ken it will be on the basis of tokenism, and the fact that the Labour leadership could not persuade one of their big guns to take on the task."
Mr Phillips' supporters said Mr Kerr's remarks were a publicity stunt.
A spokesman said: "Trevor is not standing to be the black candidate for mayor of London. He is standing to be the Labour candidate."Reuse content