He said he was offering an Al Het, a prayer said on Yom Kippur, the Jewish Day of Atonement. It signifies a plea for forgiveness.
"We must not permit criticisms for improvement to stigmatize Israel," Carter said in the letter, which was first sent to JTA, a wire service for Jewish newspapers, and provided Wednesday to The Associated Press. "As I would have noted at Rosh Hashanah and Yom Kippur, but which is appropriate at any time of the year, I offer an Al Het for any words or deeds of mine that may have done so."
Carter, who during his presidency brokered the first Israeli-Arab peace treaty, outraged many Jews with his 2006 book "Palestine: Peace Not Apartheid." Critics contend he unfairly compared Israeli treatment of Arabs in the West Bank and Gaza to the legalized racial oppression that once existed in South Africa.
Israeli leaders have also shunned him over his journey to Gaza to meet with Hamas, considered a terror group by the U.S., the European Union and Israel.
Carter's apology was welcomed by Abraham Foxman, national director of the Anti-Defamation League and a vocal critic of Carter's views on Israel.
"When a former president reaches out to the Jewish community and asks for forgiveness, it's incumbent of us to accept it," he said in a telephone interview from Jerusalem. "To what extent this is an epiphany, only time will tell. There certainly was a lot of hurt, a lot of angry words that need to be repaired. But this is a good start."
The American-Arab Anti-Discrimination Committee could not immediately be reached for comment.
The letter comes weeks after his grandson, Jason Carter, said he would run for a Georgia state Senate seat being vacated by President Barack Obama's nominee to be U.S. ambassador to Singapore. If David Adelman is confirmed as ambassador in January, Jason Carter will be a candidate in a March special election in the northeast Atlanta district.
Jason Carter, who is running in a district with a vocal Jewish population, said in a statement that his grandfather's letter was unrelated to his campaign and hailed the apology as a "great step towards reconciliation."
President Carter's letter said he hopes bloodshed and hatred will yield to mutual respect and cooperation between Israel and its neighbors. The Nobel Peace Prize laureate has long said bringing peace to the Middle East remains one of his unfulfilled goals.
In a recent appearance at Emory University, he said if he had one more day as president he would use it to bring the "full weight of the White House" to the peace process.
"That's what I'd do with my one day in the White House," he said. "Bring peace to Israel and its neighbors."