Four years ago, violence between Muslim and Buddhist communities in Burma’s Rakhine state left scores dead and entire villages smoldering in ash. Some 140,000 people, mostly ethnic Rohingya, were internally displaced, and tens of thousands more fled by land and sea to countries stretching from India to Malaysia.

As secretary-general of the Association of Southeast Asian Nations at the time, I called for a regional response to provide humanitarian assistance to the displaced and alleviate the suffering of the Rohingya. They have lived in Burma for generations but are excluded from citizenship by virtue of their ethnicity.

Neglecting their plight, I feared, would entrench the segregation of Rakhine state along ethnic and religious lines, breed conflict, and potentially radicalize a desperate minority. And it would not be Burma’s problem alone; security concerns and an outflow of refugees would implicate the entire region.

I wish I was wrong. Two months ago, a small group of alleged Rohingya militants stormed a Burmese border post in the town of Maungdaw, near Bangladesh. They staged several more attacks in the following days and weeks, killing a number of security personnel and looting weapons. This is the first time in decades that any Rohingya are suspected of taking up arms.

The Burmese military responded in force, killing dozens of suspected militants. In some cases, it burned homes in a security-clearance operation. Human-rights groups and some of the thousands of Rohingya who have fled to Bangladesh in recent weeks have said that the military response is indiscriminate and excessive, with disturbing reports of mass killings and rape.

The security operation also prevented the United Nations and other humanitarian agencies from providing lifesaving aid to tens of thousands of Rohingya. They depend on that aid because, being stateless, they have no regular access to livelihoods.

In recent weeks, peaceful demonstrations have sprung up across the region protesting Burma’s treatment of the Rohingya. But as I implored four years ago, this is not Burma’s problem alone. It is time all of us in the region accept some measure of responsibility for the Rohingya and begin working together to solve the problem.

Naysayers may point to the Asean principle of noninterference, but there is a precedent for this kind of regional cooperation. In 2008, I helped mobilize an Asean-led humanitarian response inside Burma after Cyclone Nargis tore through large swaths of the country. If that was possible when the country was still closed to the world, surely it is possible now in a newly democratic Burma.

The effort must begin inside Burma. Humanitarian and human-rights organizations should be granted unfettered access so that they can resume aid and independently investigate whether abuses have been perpetrated by the military and the militants. Basic human rights, especially the freedom of movement, should be restored to Rohingya in Rakhine state so that they can find work and go to school. Other countries can help: Malaysia and Thailand, which have done a remarkable job regularizing large groups of stateless persons, could provide guidance on how to replicate that experience for the Rohingya in Burma.

Enfranchising Rohingya is only the first bulwark against radicalization. Equal opportunity must follow. To ease intercommunal tension and build trust, the whole of Rakhine state should be integrated into Burma’s ambitious development plans, but also into the Asean Economic Community.

Helping the hundreds of thousands of Rohingya refugees in the region is also part of South and Southeast Asia’s responsibility. Almost none have a legal right to work. Malaysia has just announced a pilot work program for 300 Rohingya; other countries should follow suit so that refugees can find gainful employment, contribute to their host communities and support relatives still in Burma.

Paradoxically, the countries that have seen the largest demonstrations in support of the Rohingya—Indonesia, Malaysia and Thailand—are the same ones that pushed boats carrying Rohingya refugees back out to sea in May 2015. Thousands of Rohingya languish in immigration detention in these countries because they couldn’t obtain a passport in Burma. They had no choice, therefore, but to enter these countries illegally. We need to stop punishing them for simply exercising their right to seek asylum from persecution.

That right is enshrined in the Universal Declaration of Human Rights, adopted by the United Nations General Assembly 68 years ago this Saturday. It was the same year that the Union of Burma became an independent country. On Dec. 10, 1948, in one of its inaugural roll calls at the General Assembly, Burma was drawn by lot to cast the first vote on the adoption of the Universal Declaration of Human Rights. It voted in favor.

Burma can lead the way forward again, but only if the countries of South and Southeast Asia stand behind it. Inside the country and out, the Rohingya are our neighbors. They live in all our communities. At a time when so much of the world seems to be turning inward, ours can be one region that reaches out and embraces our diversity. Only then will the troubled history of the Rohingya stop repeating itself.

Mr. Surin is a former secretary-general of Asean and a former foreign minister of Thailand.