Injured No. 1 Serena Williams follows Azarenka in quitting Dubai

(CNN) -- Hours after losing Victoria Azarenka to injury, organizers of the Dubai Tennis Championships were dealt another major blow on Wednesday when Serena Williams also pulled out of the event.

The 31-year-old Williams, who became the oldest women's tennis player to be crowned world No. 1 on Monday, said she was forced out because of a back injury.

"I've just had some back problems the past couple of weeks," the American told an impromptu press conference.

"I thought it would get better as the week went on but it didn't. I don't want to keep pushing it and make it worse."

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Williams took to the court to apologize to fans who had arrived for her second-round match with Marion Bartoli of France.

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The absences of both Williams and previous No. 1 Azarenka represent a severe dent to a popular $2 million tournament which had already been without the sport's two reported highest earners, Maria Sharapova and Li Na (according to Forbes magazine).

It is also a blow to the Women's Tennis Association, which has worked hard to introduce incentives and regulations to reduce the number of withdrawals from its events.

Wednesday's unexpected withdrawal follows that of second-ranked Azarenka, which ensured that Williams will hang on to top spot until the Sony Ericsson Open, which starts in Miami on March 18.

Read: Azarenka out of Dubai Open

Williams said her back also troubled her in last week's Qatar Open, where she was beaten in the final by the Belorussian, who withdrew from the Dubai championships with a foot injury.

The 15-time grand slam winner added that, having returned to the pinnacle after two and a half years during which her life and career were threatened following a freak foot injury in 2010, being No. 1 is no longer her primary goal.

"OK, I have done it, let's focus on my next goals which are the grand slams," Williams said, admitting that she already had at least half an eye on the French Open in Paris, starting on May 26.

"I really want to continue doing really well in those."

After winning Wimbledon and the US Open last year, Williams' total of grand slam titles is only three fewer than Martina Navratilova and Chris Evert, who together are second on the all-time list behind Steffi Graf with 22.

Williams' absence increases the chances of world No. 4 Agnieszka Radwanska making a successful defense of her title, which began with the Pole grinding out a 7-, 6-3 win over Yulia Putintseva, a promising 18-year-old wild card entry from Kazakhstan.

Bartoli, who received a wild-card invite after making a late entry, will face former world No. 1 Caroline Wozniacki in the quarterfinals.

The Dane, now ranked 10th and a winner of the tournament in 2011, progressed with a 6-0 6-1 drubbing of China's former Wimbledon semifinalist Zheng Jie.

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