Crowds threatened to break through heavy police cordons and scuffles broke out at one ticket site as officials opened extra sales windows at the last minute, causing some fans to stampede ahead of others in a bid to buy some of the 250,000 tickets that went on sale in different parts of Beijing.

"It was so unfair," said Ji Liqiang, who had waited for 28 hours with Wang Zhenqiang, a fellow businessman from eastern Shandong province, for a chance to buy tickets to the diving competition. "Those who came late but were able to push forward got the tickets."

The two lost their place in the queue and instead of tickets to see the diving – in which China is a gold-medal favourite – they ended up with tickets to the synchronised swimming.

The official Xinhua News Agency said 30,000 people had lined up for tickets, and temperatures above 34C, coupled with the long wait, had made people impatient.

Police threw bottles of water into the crowd, dozens of ambulances stood by to go to the aid of those queuing up, and the hundreds of police and paramilitary People's Armed Police personnel were also feeling the strain.

Despite the problems, an Olympic official said the start of the sale had gone well. "There were so many people who wanted tickets, so we decided to open more ticket windows.

"In general, so far the ticket sale has gone smoothly," said Sun Weide, a spokesman for Beijing's Olympic organising committee.

For Xue Manjie, the wait was worth it. The 19-year-old and eight friends bought tickets after waiting since Thursday morning. "We can't get the tickets for the games we want but at least we can have a look inside the Water Cube and the Bird's Nest," Xue said, referring to the swimming venue and the main athletics stadium.

Xue and his friends, who had just finished their university entrance exams, wanted tickets to the basketball, but had to settle for the synchronised swimming and preliminary track and field events.

At Wukesong in the western part of Beijing, tens of thousands of people queued to buy tickets for the popular basketball competition, for which about 20,000 tickets were on sale.

The Olympics start a week on Friday and, all told, 6.8 million tickets have been available for domestic and foreign sales.

Though previous Games have had problems filling venues for the less popular events, those in Beijing are expected to be packed with enthusiastic fans. Some tickets were given away to school groups and government work units in an effort to present packed stadiums to television viewers around the world.

Organisers have said they are taking precautions against fake tickets and touts, both of which are common in China. Buyers yesterday were limited to two tickets per person.

BACKGROUND

Tickets for the Games range in price from 5,000 yuan (£370) for the opening ceremony to only 30 yuan (£2.20) for the softball preliminaries.

The sale of the 6.8 million-plus Olympic tickets on offer has been swift, but not without incident. Prospective buyers have complained on blogs and in chat-rooms of not being able to complete purchases after the third batch of tickets was released in May.

The former Olympic ticketing chief was sacked last November after the ticketing website crashed on the opening day of the second round of sales.

Police are cracking down on touts. More than 40 have been arrested, including one who was selling 50 yuan basketball tickets for 5,000 yuan.