Mr. Clooney, who advertises the Swiss watchmaker around the world, has repeatedly spoken out about the crisis in Darfur and has visited the region to draw attention to the humanitarian crisis there.
He told the BBC website, "I have talked with Omega (about China) for over a year and will continue to talk to Omega. I have and will continue to ask China to use its considerable leverage with the government of Sudan."
An Omega spokesperson said, "We have indeed discussed the Darfur issue with Mr. Clooney. We have full respect for his strong engagement in the fight for the good cause and share his opinion, especially concerning Darfur, and we are proud to work with a person who has such high ethical values."
More than 200,000 people have been killed and 2.5 million forced from their homes during five years of conflict in the Sudanese province, where pro-government Arab militias are accused of carrying out a campaign of ethnic cleansing against non-Arab groups.
China is a major trading partner with Sudan, and Beijing has resisted United Nations attempts to force Sudan to accept U.N. peacekeepers in Darfur.
The Omega spokesperson continued, "We are, of course, well aware of the controversy with respect to China hosting the games. However, political issues will always come into play regardless of where the games take place."
Omega stressed that it is not a sponsor of the games; it has been paid to provide time-keeping and data-handling services at the Olympics since 1932, including the boycotted Moscow and Los Angeles games in the 1980s.
Staying out of politics
"It is our policy not to get involved in politics because it would not serve the cause of the sport, which helps create understanding and peace all over the world. We are partners of the athletes and the I.O.C., not of governments, which is why we were present during the boycotted games of 1980 and 1984."
Omega said there is no indication Mr. Clooney might terminate his relationship with the watchmaker over the issue. In a statement, Swatch Group CEO Nick Hayek said that the "relationship with George Clooney was never as good as now," and that Mr. Clooney "wants an even closer relationship with the brand."