Speaking on HuffPost Live, the 93-year-old former Democrat US president said: "I think Jesus would encourage any love affair if it was honest and sincere and was not damaging to anyone else and I don't see that gay marriage damages anyone else."
Mr Carter - who describes himself as a born-again Christian and teaches Sunday school classes at Maranatha Baptist Church in Georgia - also spoke about his newly released book titled A Full Life: Reflections at Ninety.
The former leader, who served as president from 1977-1981, added that he would "struggle" to be pro-choice.
"I have a hard time believing that Jesus would approve abortions unless it was because of rape or incest or if the mother's life was in danger," Mr Carter said.
However, he added that he didn't question abortion's illegality when he was President: "My oath of office was to obey the Constitution and the laws of this country as interpreted as the Supreme Court, so I went along with that."
The landmark Roe v Wade decision was made by the United States Supreme Court in 1973 - four years before Mr Carter took office, legalising abortions in the US.
Meanwhile, on Tuesday President Donald Trump nominated federal appeals court judge Brett Kavanaugh to the US Supreme Court.
If confirmed by the US Senate, Mr Kavanaugh will replace long-serving conservative Justice Anthony Kennedy, who was a swing vote in favour of abortion rights.
Mr Kennedy's retirement sparked fears that the Supreme Court would roll back abortion rights for women in the US.
While Mr Kavanaugh has never publicly revealed his stance on abortion, he recently voted against giving an undocumented teenager access to an abortion while in custody.
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