King, who beat the twice-banned Russian in the 100 metres breaststroke final on Monday, showed her displeasure at Efimova competing in Sunday's heats, wagging her finger at the Russian before she called her a drug cheat.
Efimova was only allowed to compete at the Games after winning an appeal against a ban for her previous doping.
"I think people should be speaking out more. You know I think (Lily) is right. I think something needs to be done."
Efimova has been booed every time she entered the pool deck at the Rio Games while King added fuel to the fire on Sunday when the pair exchanged angry glances before she told reporters she was not happy with the Russian being able to compete.
"You're shaking your finger 'number one' and you've been caught for drug cheating," she said. "I'm not a fan.
"If that's what she feels she needs to be able to compete, whatever, that's her deal.
"I'm here to compete clean for the U.S. and that's what I'm going to do."
Phelps was full of admiration for his 19-year-old team mate.
"You know, we have some tough young kids in our team and I think that's something special," Phelps said.
"It's kind of sad that today in sports in general, not just in swimming, there are people who are testing positive and are allowed back in the sport, and multiple times.
"I think it just breaks what sport is meant to be and that pisses me off."
France's Camille Lacourt, a three-times backstroke world champion, joined the chorus after taking fifth place in the 100m backstroke final, urging the international federation, FINA, to act tough on dopers.
"I am very sad to see how my sport is evolving. It's like I'm seeing athletics, with two or three dopers in every final," he was quoted as saying by French media.
"I hope FINA will react quickly and stop this massacre because it's becoming sad. They have nothing to do in sport. I'm disgusted to see athletes who cheated on a podium."
