BANGKOK — The appointment of former senator Bob Kerrey to lead a new US-backed university in Vietnam has set off a sharp debate among Vietnamese over whether he should be disqualified because of his part in killing women and children as a Navy SEAL during the Vietnam War.

“While the Vietnamese are willing to let bygones be bygones,’’ Ton Nu Thi Ninh, Vietnam’s former ambassador to the European Union, said by e-mail, “the decision to appoint Bob Kerrey to be chairman of the board of the first American-style university in Vietnam strikes me as insensitive to the Vietnamese at best, and taking us for granted at worst.’’

The university, Fulbright University Vietnam, the first independent, private university in Vietnam, made news after President Obama announced its opening during a visit to Vietnam last week.

Kerrey admitted 15 years ago that he and the team of commandos he led in the Mekong Delta in 1969 killed innocent women and children during a midnight raid in the village of Thanh Phong. Survivors of the attack said 20 civilians were killed, including 13 children and a pregnant woman. Kerrey was awarded a Bronze Star after his squad falsely reported that it had killed 21 Viet Cong guerrillas.

Kerrey was silent about the slaughter for more than three decades until The New York Times and CBS News were on the verge of publishing a joint investigation in 2001.

“It was not a military victory,’’ Kerrey acknowledged in speech then. “It was a tragedy, and I had ordered it.’’

“I have been haunted by it for 32 years,’’ he said.

The discussion of Kerrey’s war history — which has bubbled up in posts on Facebook and in articles in online news portals — threatens to reopen old wounds from what is known in Vietnam as the American War. About 3 million people died in the war, including more than 58,000 Americans.

“I cannot look at his face,’’ Pham Thuy Huong, 40, of Hanoi, wrote on Facebook. “All the gruesome details of that genocide are still there.’’

But since the war ended in 1975, the Vietnamese government and many Vietnamese have adopted an attitude of forgiveness, and that view was also widely represented.

“It is easy to hate Bob Kerrey and ask him to resign as the head of the board of Fulbright University Vietnam,’’ Luong Hoai Nam, an aviation businessman, wrote in a column in the online newspaper VnExpress. “I can do that. But after a half day of thinking, I decided on the harder choice. That is to forgive. I forgive Bob Kerrey, and I want many Vietnamese also to forgive him.’’

Responding to questions by e-mail, Kerrey said that he would resign if he felt his role were jeopardizing the American-Vietnamese education venture. “If I have cause to believe that remaining chairman puts this project at risk, I will step down,’’ he said. “I have come to admire the Vietnamese people greatly and intend to continue doing all I can to help them.’’

Kerrey was a Navy SEAL lieutenant when he led his squad into Thanh Phong on Feb. 25, 1969. Their mission was to hunt down a Viet Cong leader. The squad encountered a hut they had not expected. To avoid giving away their position, they used knives to kill five people, witnesses said, slitting the throats of an elderly couple and stabbing their three grandchildren.

Although Kerrey has taken responsibility for ordering the killings, he has said he did not participate in them. However, two other members of his unit say Kerrey helped kill the grandfather, later identified as Bui Van Vat, 65.

When they reached the main part of the village, they encountered women and children. According to Kerrey’s account, someone fired on the squad and the commandos returned fire, killing the civilians in the darkness and confusion.

A member of his squad, Gerhard Klann, gave The Times a different account. He said the SEALs rounded up the women and children, then debated what to do. They were not in a position to take prisoners, and if they let them go the villagers might alert the enemy. So Kerrey gave the order, Klann said, and they opened fire. “The baby was the last one alive,’’ he said. “There were blood and guts splattering everywhere.’’

A survivor, Bui Thi Luom, in 2001 gave an account that matched Klann’s.

Kerrey was later wounded on another mission and lost part of a leg. He and his raiders were never held to account for the killings.

Kerrey served as Nebraska’s governor and senator, ran for president in 1992, and retired from politics in 2000. He served as president of the New School, a university in New York City, from 2001 to 2010.

Bao Anh Thai, a lawyer in Ho Chi Minh City, said that leading a university was not the proper place for a man with Kerrey’s war record.

“Please tell me the name of any prestigious university in this world, where a killer in cold blood of women and children — he admitted it and he is not charged for it — could be the president,’’ he wrote on Facebook. “It is not about the Vietnam War, it is not about reconciliation between the two countries, it is a common sense of education. Would you send your children to a university like that?’’