"China has focused on strengthening security and protection around Olympic venues and at the Olympics Village, so Beijing is already prepared to respond to any threat," Beijing Games spokesman Sun Weide was quoted as saying.
The International Olympic Committee said it also believed the Chinese authorities had done everything possible "to ensure the security and safety of everyone at the Games".
About 100,000 police and soldiers are on standby ahead of Friday's opening ceremony, and the already tight security has been stepped up in Tiananmen Square.
Security has also been beefed up in Xinjiang, Xinhua news agency said. Police intensified road checks and increased personnel at government offices, schools and hospitals in Kashgar, the agency said.
Kashgar, known as Kashi in Chinese, is some 4,000km (2,500 miles) from Beijing, near the border with Tajikistan.
Early on Monday, two men drove a rubbish truck into a group of policemen, then attacked them with grenades and knives.
The men - a taxi driver and a vegetable seller from the local area, according to Chinese media - were later arrested.
The BBC's James Reynolds at the scene of the attack that killed 16 policemen
Although the episode happened a long way away from Beijing, the very fact that it happened four days before the opening ceremony of the Olympic Games is making organisers nervous, says the BBC's James Reynolds in Xinjiang.
But, says our reporter, at the scene itself there is almost no trace of the incident, apart from three uprooted trees.
Xinjiang, in the north-west of the country, is home to the Muslim Uighur people. Uighur separatists have waged a low-level campaign against Chinese rule for decades.
Human rights groups say Beijing is suppressing the rights of Uighurs.
Last week, a senior Chinese army officer warned that Islamic separatists were the biggest danger to the Olympics.
Ethnically Turkic Muslims, mainly in Xinjiang
Made bid for independent state in 1940s
Sporadic violence in Xinjiang since 1991
Uighurs worried about influx of Han Chinese and erosion of traditional culture
Col Tian Yixiang of the Olympics security command centre told reporters the main threat came from the "East Turkestan terrorist organisation".
The term is used by the government to refer to Islamist separatists in Xinjiang.
Late last month a group called the Turkestan Islamic Party said it had blown up buses in Shanghai and Yunnan, killing five people.
But China denied that the explosions were acts of terrorism.
The Washington-based IntelCenter, which monitors terrorism communications, said the Turkestan Islamic Party had released a video entitled Our Blessed Jihad in Yunnan.
In it the group's leader, Commander Seyfullah, said it was responsible for several attacks and threatened the Olympics.
"The Chinese have haughtily ignored our warnings," IntelCenter quoted him as saying.
"The Turkestan Islamic Party volunteers... have started urgent actions."
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