In one city, Mianyang, near the epicentre, more than 18,000 people are said to be buried under the rubble, state news agency Xinhua reports.
In the nearby town of Mianzhu, at least 4,800 people are trapped, and massive landslides have buried roads to outlying villages, state news agency Xinhua says.
Sichuan Vice-Governor Li Chengyun said the death toll included: 7,395 in Mianyang, 2,648 in Deyang City, 959 in the provincial capital Chengdu, 700 in Guangyuan City, and 161 in the Aba Tibetan and Qiang Autonomous Prefecture.
Premier Wen Jiabao was quick to reach the scene and urged rescuers to clear roads into the worst-hit areas as fast as possible.
"As long as there is even a little hope, we will redouble our efforts 100 times and will never relax our efforts," he told crying locals through a loudhailer in the badly hit Dujiangyan city, south-east of the epicentre.
The health ministry has made an urgent appeal for people to give blood to help the injured.
But plans to air-drop supplies and deliver troops by parachute have been undermined by bad weather.
The BBC's Michael Bristow describes a scene of organised chaos in Dujiangyan - with dazed survivors in the streets in their pyjamas while police try to direct traffic.
China mounts huge rescue efforts to find survivors
He heard the story of one man whose uncle was trapped in the rubble of his apartment building. He was able to speak to him on his mobile phone, but could not reach him and was desperately searching for help.
Panic is rife, he says, and there is a palpable sense of fear. Strong aftershocks have hit regularly, and rumours that others are about to strike have sent people scurrying through the streets, dragging bags behind them.
People do not want to return to their homes, he says, and are spending another night in the open, in heavy rain, with no power or water.
The quake - now upgraded to 7.9 magnitude - struck on Monday at 1428 local time (0628 GMT) and was felt as far away as Beijing and the Thai capital, Bangkok.
Boulders and landslides are blocking roads in the worst-hit areas and helicopters have been unable to land because of the bad weather.
Beijing has deployed 50,000 troops to help with relief efforts, but many have not yet arrived.
About 1,300 rescue troops and medics have reached Wenchuan county and immediately started searching for survivors and treating the injured, Xinhua reported.
But there is still no word on casualties from the area - where about 100,000 people live.
Children pulled from the rubble at the school in Dujiangyan
Parents of about 900 students buried in the rubble of their school in Dujiangyan city waited anxiously for news, while relatives of at least 50 children whose bodies had been recovered mourned beneath the tarpaulin roof of a makeshift mortuary.
More than 100 people are thought to be buried underneath a hospital that collapsed. Relatives waited at the gate all day on Tuesday, but rescue workers only managed to pull out one body.
In Shifang, where two chemical plants collapsed, releasing a huge toxic cloud, about 600 people were reported dead and up to 2,300 still buried.
More than 300 people were killed in the neighbouring provinces of Gansu and Shaanxi, and in Chongqing municipality, Xinhua said.
There are also fears for the safety of staff and tourists - including a group of 19 British visitors - at a giant panda research centre at Wolong in Wenchuan.
However, after about 36 hours during which the centre could not be contacted, it emerged that at least 80 of the pandas themselves were safe, Xinhua said.
RECENT CHINA QUAKES
March, 2008: 7.2 quake in Xinjiang - damage limited
February 2003: 6.8 quake in Xinjiang - at least 94 dead, 200 hurt
January 1998: 6.2 quake in rural Hebei - at least 47 dead, 2,000 hurt
China's Olympic Games organisers say they will scale down the route of the torch through the country and there will be a minute's silence when the next leg starts in the south-eastern city of Ruijin on Wednesday.
US President George W Bush expressed condolences to victims' families, while the US, UK, the European Union, Japan, South Korea and Taiwan reportedly offered aid.
China said it would accept international help to cope with the quake - the worst since 1976 when 242,000 people were killed in Tangshan - and offered its thanks.
The government response was praised as "swift and very efficient" by Francis Marcus of the International Federation of the Red Cross in Beijing.
But he added the scale of the disaster was such that "we can't expect that the government can do everything and handle every aspect of the needs".
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