"He was quite angry with me at the time. He just said, 'Thank you Mr. President.' But he called out the name of his first grandchild, and then he called out the name of his second grandchild and he had tears running down his cheeks and so did I. Then he said in effect why don't we try one more time, and so we tried one more time and we were successful," Carter said.
The Egypt–Israel Peace Treaty was signed in Washington in March 1979, witnessed by Carter.
Relations between the two countries improved afterward, with trade agreements and airline flights. Egypt also started to supply Israel with crude oil.
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In 1980, Carter lost the election to Ronald Reagan and left the White House for his home town of Plains, Georgia, the following year.
Carter said that had he been given the chance of another term, he would have firmly implemented peace with Israel and its neighbors.
"That (peace) was never fully implemented. So now 35, 40 years later we still have Israel not at peace with its neighbors. But my successors were not very interested in the Middle East peace process, not as deeply as I was, and that's one of the things I could have done differently," he said.
CORRECTION: An earlier version misspelled Ronald Reagan's last name.