Xi, who was made general secretary of the Communist Party at the party congress last month, told Carter their countries should make all efforts to build a cooperative partnership based on mutual respect and mutual benefit, the official Xinhua News Agency reported Friday.
It was the first time Xi had met a senior U.S. politician since his elevation, which also includes becoming head of the central military commission.
Carter was accompanied by his wife, Rosalynn, on his China visit.
The U.S. visitor earlier met with China's second in command, Vice Premier Li Keqiang.
Li, expected to succeed Wen Jiabao as Chinese premier in March, told Carter: "As long as the two countries respect each other, manage differences and expand common ground, they can seek common prosperity."
Li affirmed China's commitment to deepening reform, further opening up, promoting sustainable and healthy economic development and promoting social progress, and urged Carter to use of his influence to explain the real China to U.S. leaders and public.
Carter hailed the progress China has made and praised U.S.-China relations over the past decades. He said that as an old friend of China he was committed to boosting bilateral cooperation, the reports said.