In an interview with CNN's Becky Anderson, the 92-year-old former occupant of the Oval Office urged Trump to put "peace and human rights" at the "forefront of all his discussions with foreign leaders."
Trump is set to visit Saudi Arabia, Israel and the Vatican in the coming days. According to his aides, this inaugural tour is designed as a symbolic display of commitment to US allies.
Carter, who now runs a human rights foundation in Atlanta, warned that global "protection of human rights has deteriorated greatly in the last two or three years." He chalked it up to "an absence of leadership even more from the United States in being a champion of human rights."
Trump's Israel visit
Trump has previously said he wants to work for Middle East peace, which he has said "frankly, maybe not as difficult as people have thought over the years."
Back in February, Trump indicated that he would be willing to explore all avenues to strike what he has described as the "ultimate deal" for peace in the region.
And Carter, who ushered in the historic Israeli-Egyptian peace treaty -- also known as the Camp David Accords -- during his tenure, knows all too well the challenges Trump now faces in marshaling the Arab-Israeli peace process forward.
"I hope that President Trump will make progress in the dispute between Israel and the Palestinians and that he will bring justice to the Palestinians and alleviation of their long-term -- 50-year now -- suffering as an occupied territory," Carter told CNN.
"Of course, the Palestinians also have to be willing to recognize Israel as a nation living side by side with them in peace," the elder statesman added.
Talks between Israel and the Palestinians have stalled in recent years -- the most recent round fell apart in April 2014.
Talking to North Korea
Carter also said he believed that the US "should have communication with (North Koreans) and still insist on the overall compliance, even by North Korea, of the basic principles of peace and human rights."
The 39th President of the United States has visited North Korea three times since he left office. In 1994, he met the late Supreme Leader Kim Il Sung, grandfather of current leader Kim Jong Un.
"I spent a lot of time talking to their leaders in North Korea," he said, adding "... what they want is reassurance that they will not be attacked."