King slammed Efimova on Sunday for being caught "drug cheating" and stated that she was "not a fan" of the Russian swimmer, reports Sputnik.
Finishing first in the women's 100m breaststroke on Monday, King did not congratulate Efimova but hugged fellow American swimmer Katie Meili, who won bronze.
"If I had been in Yulia's position, I would not have wanted to be congratulated by someone who was not speaking highly of me. So if she was wishing to be congratulated, I apologise," King told reporters.
She also congratulated Efimova on a "fantastic swim" as well as expressed her readiness to compete with the Russian swimmer in the future.
On the eve of the Rio Olympics, Efimova was cleared by the International Swimming Federation to take part in the competition, successfully winning her appeal against a doping ban imposed in July.
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