"We have strengthened security work in all Olympic venues and in the Olympic village. We are well-prepared in security for the upcoming Games," said Sun Weide, spokesman for the Beijing organising committee.
The attack, a stunning embarrassment to the authorities whose intelligence had been warned of possible attacks this week, took place in Kashgar, a remote outpost of Chinese rule in the west of Xinjiang province not far from the border with Central Asia, Afghanistan and Pakistan.
Xinjiang's Muslim, ethnic Uighur, population have a history of clashes with the authorities, but there have been no major confirmed terrorist incidents since a wave of bombings in the 1990s.
The authorities have repeatedly warned of the risk of attacks on the Olympics by Islamic and "separatist" groups based in the region, though they also insisted that security in the region was under control.
Chinese state media said that two men drove a dump-truck at a group of policemen out for early morning exercise, crashed to a halt and threw grenades or home-made explosive devices. They then began slashing at survivors with knives before being overwhelmed and arrested.
Fourteen policemen died at the scene, two more died on the way to hospital, and 16 others were injured. Debris from five explosive devices was also recovered, the reports added.
Tourists in Kashgar, a Silk Road city that was a central location of the "Great Game" played out 100 years ago between the Russian and British empires for control of central Asia, said they heard loud bangs, and then were kept in their hotels while searches were carried out.
Timothy O'Rourke, an American, said the authorities had cleaned the site but the damage remained visible. "You can see there are windows that are broken in a nearby building and a pole has been ripped out of the ground," he said. "You can see some wires hanging from another pole nearby," he said.
Although no group claimed responsibility, connections will be made with a video posted on a website 10 days ago by a group calling itself the "Turkestan Islamic Party" (TIP). East Turkestan is the name under which Xinjiang briefly declared independence in the 1940s before being reconquered by Chairman Mao's People's Liberation Army.
In the video, "Commander Seyfullah" claimed responsibility for a number of small but lethal bus bombings in China in recent months, and said "critical points" for the Olympics would be targeted with further attacks. China denied the group claims, and said there was still no evidence yesterday's attacks had an Olympic connection.
The International Olympic Committee said it had confidence in Beijing's security preparations for the Games.
Exile groups such as the World Uighur Congress previously accused the authorities of exaggerating and manufacturing the terrorist threat to justify indiscriminate arrests and repression in the region.
Last night, its European representative, Dilxat Raxit, said telephone reports from the region confirmed the incident. He said the Congress opposed violence, but he accused the Chinese of provoking a response.
Uyghur Policeman?
"We do not wish to see such events, nor would we want a repeat," he told The Telegraph last night. "But we cannot prevent Beijing's systematic suppression of the Uighur people, nor are we able to control such acts as these. The Chinese authorities' policies and behaviour force Uighurs down the road towards millitary action and attack."
One Uighur terrorist group, the East Turkestan Islamic Movement (ETIM), which may be the same as the TIP, is accused by both the United States and China of links to al-Qaeda. Its numbers are unknown, and it was at one time thought to have disintegrated after its leader was killed in Pakistan in 2003.
Analysts say no Uighur group is thought to be sophisticated enough to penetrate the ring of steel which the Chinese authorities have thrown around Beijing for the Games, deploying more than 100,000 security personnel.
Nevertheless, in a separate incident in Beijing itself, a small group of protesters clashed with police near Tiananmen Square. They were local residents who had been evicted from their homes just south of the Square to make way for a new shopping district.
They were surrounded but not arrested by police, who are deeply sensitive about any form of demonstration on the Square. Eventually they were led away by members of the local neighbourhood committee, the lowest reaches of the Communist Party.