In a rambling, three-page letter to Obama obtained by The Associated Press, Gaddafi implored Obama to stop the NATO-led air campaign, which he called an "unjust war against a small people of a developing country."
"You are a man who has enough courage to annul a wrong and mistaken action," Gadhafi wrote in the letter that was sent to the State Department and forwarded immediately to the White House, according to a US official who had seen the letter.
"I am sure that you are able to shoulder the responsibility for that. To serving world peace ... Friendship between our peoples ... and for the sake of economic, and security cooperation against terror, you are in a position to keep NATO off the Libyan affair for good," Gaddafi wrote.
White House press secretary Jay Carney confirmed that the White House received a letter from Gaddafi.
As for Gaddafi's appeal for a cease-fire, Carney appeared to dismiss it for now.
"The conditions the president laid out are clear," Carney told reporters traveling with Obama to New York.
In the letter, sent today, addressing Obama as "our son" and "excellency," Gaddafi says his country had been hurt more morally than physically by the NATO campaign and that a democratic society could not be built through missiles and aircraft.
He also repeated his claim that his foes, particularly those now in control of the city of Benghazi, are members of al-Qaida.
The letter, in stilted and formal English, includes numerous spelling and grammatical errors.
"Our dear son, Excellency, Baraka Hussein Abu oumama, your intervention is the name of the USA. is a must, so that Nato would withdraw finally from the Libyan affair," Gaddafi wrote. "Libya should be left to Libyans within the African union frame."
Gaddafi said his country had already been unfairly subjected in 1986 to "a direct military armed aggression" ordered by then-President Ronald Reagan, who famously called the leader the "Mad Dog of the Middle East," as well as earlier rounds of US and international sanctions.
Although he listed a litany of complaints, Gaddafi said he bears no ill will toward Obama.
"We have been hurt more morally (than) physically because of what had happened against us in both deeds and words by you," he wrote.
"Despite all this you will always remain our son whatever happened. We still pray that you continue to be president of the USA. We Endeavour and hope that you will gain victory in the new election campaigne." The letter, dated April 5, 2011 in Tripoli is signed by "Mu'aumer Qaddaffi, Leader of the Revolution."