He said that one state was "obviously the goal of Israeli leaders who insist on colonising the West Bank and East Jerusalem".
However, he added: "A majority of the Palestinian leaders with whom we met are seriously considering acceptance of one state, between the Jordan River and the Mediterranean Sea.
'Nonviolent struggle'
"By renouncing the dream of an independent Palestine, they would become fellow citizens with their Jewish neighbours and then demand equal rights within a democracy.
"In this nonviolent civil rights struggle, their examples would be Mahatma Gandhi, Martin Luther King Junior and Nelson Mandela."
Carter, who commented that a two-state solution was "clearly preferable", said that Palestinian leaders had also considered the current demographics of Israel and the occupied Palestinian territories.
"Non-Jews are already a slight majority of total citizens in this area, and within a few years Arabs will constitute a clear majority," he said.
The 39th US president had been travelling in the region as a member of the Elder's Panel, a group of noted international diplomats working to address humanitarian issues.