In a letter to the city Arizona Corporation Commission member Gary Pierce said: "If an economic boycott is truly what you desire, I will be happy to encourage Arizona utilities to renegotiate your power agreements so Los Angeles no longer receives any power from Arizona-based generation.
"I am confident that Arizona's utilities would be happy to take those electrons off your hands.
"If, however, you find that the City Council lacks the strength of its convictions to turn off the lights in Los Angeles and boycott Arizona power, please reconsider the wisdom of attempting to harm Arizona's economy." Mr Pierce said if Los Angeles was "serious" about its boycott and not just "posturing" then it would have to consider supplying its own power.
The electricity comes from coal-fired power plants in northern Arizona, a nuclear power plant outside Phoenix, and two hydroelectric plants on the Colorado River.
A statement issued on behalf of Los Angeles mayor Antonio Villaraigosa said: "The mayor stands strongly behind the city council and he will not respond to threats from the state that has isolated itself from an America that values freedom, liberty and basic civil rights." Mr Villaraigosa was in Washington for a meeting between President Barack Obama and Mexican President Felipe Calderon, which was overshadowed by the Arizona law.