He hugged Manh warmly at the end of the two-hour meeting.
"Vietnam is a country that we will never forget," Castro said, who visited Hanoi in 1973 during the Vietnam war.
Manh said Castro spoke at length about Cuba's "energy revolution" to save electricity, and they discussed the situation in Latin America.
The Cuban leader looked healthier and more alert than in the last video images shown of him in Cuba on January 30 during a visit by Hugo Chavez, the Venezuelan president.
"He was very happy. I was overcome with emotion. He spoke about many things. They were very deep," Manh said afterwards at a meeting with Carlos Lage, Cuba's vice president.
Castro's exact ailment and condition remain state secrets, but he is largely believed to suffer from diverticular disease, which forms sacs in the colon that can become inflamed and bleed.
In one of a new series of essays he has been writing during his convalescence, Castro said he had undergone numerous operations and the first one had not gone well, explaining why his recovery has been delayed.
Nevertheless, senior Cuban officials have repeatedly said Castro is on the mend and the government has occasionally released photographs and videotapes during his recovery.
State television reported that Castro's meeting with Manh "ratified the warm ties that unite our nations."
Raul Castro, who is also the county's defence chief, and Manh had earlier signed a series of bilateral accords, including one that will make Vietnam Cuba's latest partner in oil exploration and drilling in the Gulf of Mexico.