David Mitchell was told of his father's death by British diplomats after he was freed with his wife, Carolyn, and son, Ben, 14, from a two-week ordeal.
The family were kidnapped by members of the Beni Dabiyan tribe who demanded a ransom and improved local facilities from the Yemeni government. In spite of the experience, Mr Mitchell, a teacher with the British Council, said he would return to finish his contract.
"I don't feel any resentment towards the country and no resentment towards the people who have been imprisoning us in the last few days," he told BBC Radio 4's Today programme.
"We are going home to England for a while - I don't know how long - and then I intend to come back and see out my contract here."
David Pearce, deputy head of the British Mission, said Mr Mitchell's brother had written telling him about the death of their father, who has not been named. He had been seriously ill for some time.
"It was one of the first things we told him," Mr Pearce said, adding that the family had been well treated except for an incident when Ben had been struck with the butt of a rifle. "I think the whole event has been distressing and [the death] is another event that added to that."
The family were kidnapped on 17 April as Mr Mitchell drove his wife and son to the airport near Sanaa, the capital. They live in England and had been visiting for Easter.
"We were driving along a straight section of the road and suddenly a Jeep slewed across the road in front of us," said Mr Mitchell. "Four armed men jumped out and effectively blocked the road, so we had to stop.
"As we saw them in front, my reaction was `Oh no! I know what's happening and it's happening to us'.
"It has to be said that the treatment was very good. They were extremely generous, very kind, very thoughtful and we never had any fear for personal safety at any time."Reuse content