By Mark Trevelyan

RIO DE JANEIRO (Reuters) - Russia's Yulia Efimova, who won her appeal against a doping ban on the eve of the Rio Olympics, swam the second-fastest time on Sunday in the heats of the women's 100 meters breaststroke.

Efimova, the world champion at the distance, clocked 1 minute 5.79 seconds, a hundredth of a second behind American Lilly King whose compatriot Katie Meili was third in 1:06.00 with holder Ruta Meilutyte of Lithuania fourth in 1:06.35.

Some jeers rang out in the Olympic Aquatics Stadium after Efimova's heat.

Revelations of state-sponsored Russian doping overshadowed the build-up to the Olympics, and the country was banned on Sunday from the Paralympics that will follow. Efimova was one of a number of Russians who successfully appealed, arguing that after serving previous doping bans they should not be punished again by being excluded from Rio.

The 24-year-old, the world champion at 100m, only learned on Friday that she could compete, ending months of uncertainty.

"I was crazy, like, last half-year, I just don't understand what's going on and everything. I'm just happy to be here and I'm ready to race," she said.

Efimova's involvement is a delicate issue with her rivals.

Asked about the prospect of meeting her in Monday's final, King said: "You know I think it's unfortunate we have to deal with these things in the sport, but both Katie (Meili) and I were very prepared for her to be swimming so we're just going to race her just like we would normally."

Pressed on whether it was fair that Efimova was competing, she said: "You know, I'm going to stay out of it, but a level playing field would be preferred."

Meilutyte declined to comment on her rival's reinstatement. Britain's Chloe Tutton, who swam in Efimova's heat, was ushered away by her press minder when asked how she felt about the Russian's involvement.

Efimova is also due to compete in the 200m breaststroke, in which she was world champion in 2013 and won a bronze medal at the London Olympics in 2012.

Efimova was banned between October 2013 and February 2015 after testing positive for traces of the anabolic steroid DHEA. She was also briefly suspended after testing positive for meldonium this year, but cleared in July.

Meldonium was added to the World Anti-Doping Agency's list of banned substances from Jan. 1, but some positive tests were later overturned after WADA said there was a lack of clear scientific evidence about how long it takes for the drug to be excreted from the body.

(Reporting by Mark Trevelyan; Editing by Ken Ferris and Alison Williams)