The day before he was fired from his National Security Council staff job last November, Marine Lt. Col. Oliver L. North offered to resign, according to evidence made public yesterday at hearings of the joint congressional committees investigating the Iran-contra affair.

North, in a computer message to his boss, then-national security adviser John M. Poindexter, said he remained confident the secret Iran-contra operations that were then becoming public had been worth the risk, but foresaw a bout of "political fratricide."

In the Nov. 24 message, North wrote: "There is an old line about, 'You can't fire me, I quit.' I am prepared to depart at the time you and the president decide it to be in the best interests of the presidency and the country.

"I am honored to have served the president, you, and your predecessors, these past 5 1/2 years. I only regret that I could not have done so better.

"My prayer is that the president is not further damaged by what has transpired, and that the hostages will not be harmed as a consequence of what we now do.

"Finally, I remain convinced that what we tried to accomplish was worth the risk.

"We nearly succeeded, and hopefully, when the political fratricide is finished, there will be others, in a moment of calm reflection, who will agree," North concluded.