Guor Marial, 28, who was born in southern Sudan at the start of the conflict, would have liked to run the marathon for South Sudan, which became an independent country last year.
The world's newest country has not yet established a National Olympic Committee, however, so it cannot send a team to the Games, which open next week.
The International Olympic Committee (IOC) has suggested that Marial runs for Sudan, which has invited him to join their team, the runner told AlertNet, a humanitarian news service run by Thomson Reuters Foundation.
Marial, who lost 28 members of his family in the war, has refused.
"I lost my family and relatives, and in South Sudan two million people died," he said by telephone from Flagstaff, Arizona, where he lives.
"For me to just go and represent Sudan is a betrayal of my country first of all, and is disrespecting my people who died for freedom."
South Sudan gained independence last July after a 2005 peace deal ended more than two decades of war between the mostly Christian south and Arab north. Tensions remain high following clashes in contested borderlands and rows over oil payments.
Rights group Refugees International (RI) wrote to IOC President Jacques Rogge on Tuesday to request that Marial be allowed to compete as an independent under the Olympic flag.
"Numerous members of Mr Marial's family have been killed by Sudanese security forces, and he himself has suffered serious physical abuse at the hands of Sudanese police," RI President Michel Gabaudan wrote.
"The threats against him are serious and were recognised as such when he gained refugee status in the United States. Therefore, asking Mr Marial to submit once again to Sudanese authority as an Olympic athlete is not acceptable."
The IOC was not immediately available for comment.
Marial cannot race for the United States, even though he has permanent residency, because athletes have to be full citizens of the countries they represent.
In a marathon in San Diego, California, last month Marial ran a personal best, finishing in two hours 12 minutes 55 seconds.
"If I did get permission to run in London, the shape I'm in right now, I think I might be in the top 15 to 20," said the chemistry graduate, who works with people with mental disabilities when he is not training.
Marial left Sudan at the age of 14 following an attack when Sudanese soldiers entered his home at night. He was knocked unconscious when a soldier smashed his jaw with a rifle.
The athlete, who arrived in the United States when he was 16, said he appreciated Sudan's offer but it was impossible to accept.
"In my situation, the consequences of me representing Sudan are bigger than me going to the Olympics," he said in the interview late on Tuesday.
"At this level, as an athlete, I don't just represent my family, but the whole of South Sudan. It's a very heavy responsibility to carry. It's very important for me to make the right decision," he added.
"My dream is to represent South Sudan. It's just a matter of time." (Reporting by Tim Large; Editing by Clare Fallon)