Marshall Islands President Christopher Loeak bid Jose Salvador Alvarenga farewell at the airport.
"Thank you for the support, the support by your people," Alvarenga told him in Spanish in a soft voice.
Alvarenga, clean-shaven and walking without assistance, said he was "doing very well."
He told officials during his two-week recuperation at a hospital and a hotel in the capital, Majuro, that he left Mexico in late 2012 with another fisherman, who later died, when a storm threw them off course and he drifted across 6,500 miles (10,500 kilometers) of open ocean. He said he survived on fish, birds and turtles.
About 50 officials, volunteers and reporters gathered at the airport to see him off. He was flying first to Hawaii and then on to El Salvador to be reunited with his family.
Alvarenga, accompanied by Diego Dalton, an official from El Salvador's embassy in Tokyo, said that people of the Marshall Islands were "very good" to him, and called them "my very good friends."
Alvarenga's spritely appearance a week ago while greeting hundreds of well-wishers in Majuro had many questioning his story. But he looked much weaker Thursday during a brief public appearance at the hotel, and had to be assisted into the room by two people while others stood by ready to help.
His family in El Salvador has spoken to him by phone since the story broke out. Alvarenga's 14-year-old daughter, Fatima, said last week that she didn't remember ever seeing her father, who left El Salvador when she was just over a year old.