Playing her first match since winning the Australian Open last month, top seed Li was pushed to three sets by Magdalena Rybarikova but eventually eased past the Slovak to post a 6-1 5-7 6-2 victory.

The Chinese world number three will next meet Petra Cetkovska who saw off Li's compatriot Zhang Shuai 6-3 4-6 6-3.

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Second seeded Radwanska's path to the last 16 was slightly more straightforward after the Pole raced through the second set of her match against Sorana Cirstea to win 7-5 6-0 and set up a date with Mirjana Lucic-Baroni, a 6-4 6-1 winner over Anastasia Pavlyuchenkova.

Radwanska, a semi-finalist at this year's opening Grand Slam in Melbourne, won 70 per cent of points in the second set.

Third seed Petra Kvitova edged Venus Williams in a tight encounter 6-2 2-6 7-6(7) while fourth seed Sara Errani had no major problems in a 6-0 6-4 win over Hsieh Su-Wei.

Jelena Jankovic, Angelique Kerber and Simona Halep joined the procession of seeds through to the third round, but there was disappointment for Caroline Wozniacki - who rounded off the top tier of seeded players in eighth - and second-tier seeds Ana Ivanovic and Sam Stosur.

Qatar Open results

Second round

2-Agnieszka Radwanska (Poland) beat Sorana Cirstea (Romania) 7-5 6-0

Yanina Wickmayer (Belgium) beat 8-Caroline Wozniacki (Denmark) 6-4 7-5

7-Simona Halep (Romania) beat Kaia Kanepi (Estonia) 6-4 3-6 7-6(5)

Petra Cetkovska (Czech Republic) beat Zhang Shuai (China) 6-3 4-6 6-3

Jana Cepelova (Slovakia) beat 12-Samantha Stosur (Australia) 6-4 4-6 6-1

3-Petra Kvitova (Czech Republic) beat Venus Williams (U.S.) 6-2 2-6 7-6(7)

Monica Niculescu (Romania) beat Bethanie Mattek-Sands (U.S.) 6-1 3-6 6-3

Lucie Safarova (Czech Republic) beat Peng Shuai (China) 6-2 5-7 6-4

5-Jelena Jankovic (Serbia) beat Karin Knapp (Italy) 6-0 6-2

Klara Zakopalova (Czech Republic) beat 9-Ana Ivanovic (Serbia) 4-6 6-1 6-3

6-Angelique Kerber (Germany) beat Karolina Pliskova (Czech Republic) 7-6(2) 6-4

Mirjana Lucic-Baroni (Croatia) beat Anastasia Pavlyuchenkova (Russia) 6-4 6-1

Annika Beck (Germany) beat Tsvetana Pironkova (Bulgaria) 6-7(5) 6-2 6-2

1-Li Na (China) beat Magdalena Rybarikova (Slovakia) 6-1 5-7 6-2

Alisa Kleybanova (Russia) beat Stefanie Voegele (Switzerland) 6-3 6-2

4-Sara Errani (Italy) beat Hsieh Su-Wei (Taiwan) 6-0 6-4

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