Maj. Gen. Suharto, holding stick at front left, in 1965. General Suharto helped crush the Communist movement in Indonesia and went on to rule the country from 1967 to 1998. CreditAssociated Press 

JAKARTA, Indonesia — Indonesia’s president has instructed his government to investigate one of the country’s darkest periods, the bloody anti-Communist purges of the mid-1960s, perhaps ending decades of official reluctance to confront the military’s killings of hundreds of thousands of people.

One of President Joko Widodo’s most senior ministers, Luhut B. Pandjaitan, said at a news conference Monday night that the president had told him to begin gathering information about mass graves that are said to be scattered across the Indonesian archipelago. Haris Azhar, the head of an Indonesian research organization, said on Tuesday that the government had begun contacting his group and others about the data.

The purges of 1965-66, in which hundreds of thousands of people are believed to have been killed by the Indonesian military and others, have remained an extremely delicate issue for senior government officials, many of whom were generals.

Mr. Luhut, a retired general who is now the coordinating minister for political, legal and security affairs, appeared to cast doubt on the need for an investigation into the mass graves. “The president asked me to find them, if there are any,” he said in his remarks on Monday night.

“During these decades we have always been told several hundred thousand people died, yet, until today, we have not found one mass grave,” Mr. Luhut told reporters at the presidential palace in Jakarta, the capital. Human rights organizations say there is clear evidence of such graves.

The purges followed a failed uprising by members of the Indonesian military in September 1965, as the Cold War was escalating in Southeast Asia. Top commanders called it an attempted coup orchestrated by the then-powerful Indonesian Communist Party, working with rogue military personnel.

The killings that ensued were carried out by soldiers and military-backed civilian, paramilitary and religious groups. Half a million people or more are estimated to have been killed, and hundreds of thousands of others were held in detention for years. The victims included intellectuals, ethnic Chinese Indonesians and countless others, many of whom had no connection to Communism.

Mr. Azhar, the coordinator of the nongovernmental organization Commission for Missing Persons and Victims of Violence, said his organization alone had collected evidence of at least 16 mass graves containing as many as 40 bodies each, mostly on the main Indonesian island of Java, but also on Bali and Sulawesi.

Last week, the government supported a symposium in Jakarta on the purges, the first time that a public discussion of the atrocities had received official endorsement. Some hoped it would be a first step toward an official reckoning, but others worried that the government would use the forum as an excuse to consider the subject closed.

Mr. Haris said the government had begun canvassing groups like his for their research on the period. But it was not clear what would be done with the information, he said.

“This is the issue,” Mr. Haris said. “How will the data be used?”

Another crucial issue, he said, is whether people who come forward will be protected from potential reprisals. Many of the military, political and religious groups implicated in the killings are part of Indonesia’s political elite.

Survivors of the purges hope the beginning of an investigation will allow them to confront their former tormentors, even if the new process does not lead to criminal prosecutions, said Bedjo Untung, the leader of a victims’ group known locally as YPKP 65.

“We want to make peace between the victims and the perpetrators,” said Mr. Bedjo, who was captured and tortured by the military on suspicion of being a Communist in 1970, and spent nine years in prison. “We will accept reconciliation but hope for a judicial process,” he said.

While Indonesia has made progress in coming to terms with its past during its transition to democracy, many gains have proved fleeting. Mr. Joko’s rise to the presidency in 2014 raised hopes among many Indonesians that longstanding human rights issues, such as the silence over the purges, would be addressed.

But Mr. Joko’s government has not followed up on a 2012 report by the country’s independent National Commission on Human Rights calling for criminal investigations into the purges. At the symposium last week, Mr. Luhut ruled out a criminal investigation of the killings.

“I try to be optimistic,” Mr. Haris said. “So many efforts have been ignored by the government before. I have to be careful.”

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