The commander of the nuclear submarine Greeneville, which sank a Japanese fishing trawler 19 days ago, has delivered letters of apology to the families of the nine people lost, the trawler's skipper and Japanese officials, Japanese and Navy officials said today.

The commander, Scott D. Waddle, visited the consulate here on Tuesday afternoon to apologize and to deliver the letters, which he wrote himself, the officials said.

In a meeting with Yoshio Mochizuki, a vice minister in the foreign ministry who was visiting from Tokyo, Commander Waddle, who was dressed in a business suit and was alone, made a traditional deep bow and said a few words in Japanese. Commander Waddle explained that he had been born in Misawa, Japan, when his father was an Air Force officer there. It was there that he learned to speak some Japanese, he said.

''When Waddle handed the letters to me tears fell from his eyes,'' Mr. Mochizuki told Japanese reporters at the airport before his departure for Tokyo today. ''He repeated over and over to me his words of apology.'' He added that Commander Waddle had ''used the word apology so I accepted it as an apology.''