The head of the International Olympic Committee, Jacques Rogge, has praised Beijing's "extraordinary" efforts to cut pollution ahead of the Games.
He said there would be no danger to the health of athletes, despite continuing concerns about pollution levels.
He was speaking as dignitaries from around the world gathered in China's capital for Friday's opening ceremony.
Among them is US President George Bush, who earlier expressed "deep concerns" about Beijing's human rights record.
Speaking in the Thai capital, Bangkok, before travelling to the Games, Mr Bush praised China's economy but said only respect for human rights would let it realise its full potential.
China rejected Mr Bush's criticisms as "interference" in its internal affairs.
Air target missed
A day before the Games, a BBC reading suggested Beijing's air quality was far below World Health Organization (WHO) standards.
It put levels of particulate matter (PM10) at 191 micrograms per cubic metre. This far exceeds the WHO target of 50 micrograms/cubic metre, and also exceeds the WHO target for developing countries of 150 micrograms/cubic metre.
Beijing pollution: Facts and figures
But Mr Rogge praised the Chinese authorities for having done "everything that is feasible and humanly possible to address this situation".
"What they have done is extraordinary," Mr Rogge told reporters.
He said there was "absolutely no danger" to the health of athletes taking part in events that last less than one hour. But he said if the pollution was bad, events which lasted more than that could be shifted or postponed.
Mr Rogge urged reporters to distinguish between fog and pollution - a point, correspondents say, often made by Chinese authorities.
"The fog, you see, is based on the basis of humidity and heat. It does not mean that this fog is the same as pollution," he said.
He also said that China's efforts to clean up the air around Beijing would "continue and have a lasting influence on the climate of Beijing".
Separately, Mr Rogge said athletes would be prevented from making any political statement or protest in official venues - in accordance with Rule 51 of the Olympic charter, which forbids athletes from making political, religious, commercial or racial propaganda.
But he said they were free to do this in protest areas provided by Chinese authorities, and that "common sense" would be used to judge violations.
He spoke after more than 40 Olympic athletes signed an open letter to President Hu Jintao urging China to respect freedom of opinion and religion, particularly in Tibet.
The letter urged China "to protect freedom of expression, freedom of religion and freedom of opinion in your country, including Tibet".
"America stands in firm opposition to China's detention of political dissidents, human rights advocates and religious activists "
Issued by Amnesty International and the International Campaign for Tibet, it also called on President Hu "to ensure that human rights defenders are no longer intimidated or imprisoned" and "to stop the death penalty".
There were celebrations on Thursday as the Olympic torch began making its last stops on a journey that has seen it pass through five continents.
Patriotic crowds lined the mist-shrouded Great Wall waving fans and cheering, while streams of confetti shot into the air as the torch was lit from the Olympic flame.
The torch, while welcomed in many nations, has also been a magnet for protesters critical of China's respect for rights.
Mr Bush hit out at China's "detention of political dissidents, human rights advocates and religious activists" before he arrived in China for the opening ceremony.
But China offered a robust defence of its record in response, insisting it "put its people first".
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