Serena Williams has said she is still at the beginning of a long comeback after her second-round defeat by Petra Kvitova in Cincinnati.

The 6-3, 2-6, 6-3 loss to the eighth seed and two-time Wimbledon champion followed her first-round exit in San Jose two weeks ago, when she suffered her heaviest career defeat, at the hands of the British No 1, Johanna Konta. Cincinnati was Williams’s sixth tournament since giving birth last September. She has dealt with blood clots and recently said she has been struggling with postpartum emotions.

Andy Murray comeback hits another bump with first-round loss in Cincinnati Read more

“You know, this is a long comeback,” Williams said. “I just began. I just started – definitely at the very, very beginning. I’m getting there, and I’m going to just continue to work hard, and hopefully, I’ll start winning more matches.”

Kyle Edmund also went out in the second round, losing in straight sets to the 19-year-old Canadian Denis Shapovalov. After surviving five match points, the British No 1 eventually succumbed 6-4, 7-5. The world No 16 will continue his US Open preparations at the Winston-Salem Open, which begins on Saturday.

Roger Federer, however, enjoyed a successful return to the Tour, overcoming Germany’s Peter Gojowczyk 6-4, 6-4, and said the victory helped consign his Wimbledon quarter-final defeat by Kevin Anderson to history. The 37-year-old, who follows a limited schedule to prolong his career, has not played since his earliest exit at the All England Club since 2013.

“It’s nice to have played so that my last match was not the Anderson match,” Federer said. “You’ve kind of turned the page. It’s a good thing. The goal is now to recover from this match, take the positives with me. Of course the big goal is the US Open.”

It was the world No 2’s first appearance at the tournament since winning the title in 2015. “It doesn’t feel like I have been away for so long here from Cincinnati,” he said. “I guess the wheel keeps turning. It’s not like I missed two years of tennis. It was a great pleasure to be back.”

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Karolina Pliskova and Nick Kyrgios also advanced on Tuesday. Pliskova, the former world No 1, moved into the second round by snapping a seven-match losing streak against Agnieszka Radwanska with a 6-3, 6-3 win.

“It means a lot because it was against her and I never beat her,” Pliskova said. “We played so many times. I think I always played her at her best level the matches before, so it was always tough.”

Kyrgios, a finalist last year in Cincinnati, overcame physical problems to fight off the qualifier Denis Kudla for a 6-7 (2), 7-5, 7-6 (9) victory.

“This year has been tough,” Kyrgios said. “I started the year very well. Then I hurt my elbow. Then I had an ongoing hip injury. We have been definitely thinking about the options with my hip. You know, there is only so much you can do before you have to get surgery or something like that. Right now I’m just managing it.”

The Australian Open semi-finalist Hyeon Chung won the last five games to beat Jack Sock 2-6, 6-1, 6-2. Sock has lost eight consecutive matches since May. Milos Raonic, a two-time Cincinnati semi-finalist, advanced with a 6-3, 6-3 win over the qualifier Dusan Lajovic.

Caroline Garcia reached the third round with a 6-4, 7-5 victory over the wildcard Victoria Azarenka, Australia’s Ashleigh Barty beat Marketa Vondrousova 6-3, 7-5, while Maria Sakkari upset the Indian Wells champion Naomi Osaka 6-3, 7-6 (8).