ON THURSDAY the United Nations’ designated human rights envoy to Burma will present to the General Assembly the final report of his six-year term. Tomás Ojea Quintana, a lawyer from Argentina, will celebrate the improvements he has seen over the course of his eight visits to the Southeast Asian nation also known as Myanmar. But he also will describe how far the nation of some 50 million people needs to go. The United Nations, like the United States, should heed his message and continue to encourage Burma toward freedom and democracy.

Progress has been remarkable in what was until recently one of the most repressive regimes in the world. Hundreds of political prisoners have been freed. Independent media have sprung up. The political opposition, led by Nobel Peace Prize winner Aung San Suu Kyi, has been allowed partway into government. Tentative cease-fire agreements have been signed with leaders of several ethnic groups with whom the regime had warred for decades.

“All of this is very good news,” Mr. Ojea Quintana, officially the special rapporteur on the situation of human rights in Myanmar, told us recently. “At the same time, there are very serious human rights shortcomings, and this is what the international community needs to remember and focus on.”

In some ethnic areas, regime violence continues, and hundreds of thousands of uprooted people remain displaced. There has been no accountability for official crimes of killing, disappearances and torture. Some longtime political prisoners remain in prison; new ones — notably people who have peacefully protested land seizures — have been thrown in jail; and all releases have been conditional. Terrible violence by Buddhists, the majority in Burma, against Muslims has been officially tolerated, if not sanctioned. Many undemocratic laws remain in force, the judiciary is not independent and a promise to allow a U.N. High Commissioner for Human Rights office to open has not been fulfilled. The constitution must be changed if there is any chance of a free and fair election in 2015, which Mr. Ojea Quintana called perhaps the most important question.

The General Assembly, after receiving Mr. Ojea Quintana’s report, will craft a new resolution. It should confirm the importance of U.N. engagement in Burma’s transition. Early next year, the U.N. Human Rights Council will decide whether to appoint a new rapporteur; the answer should clearly be yes.

Mr. Ojea Quintana told us that the reforms initiated by Burma’s longtime military rulers constitute “a transition that intends to bring commercial engagement,” and that the United States and European Union are focused on those commercial opportunities. He said he favors economic development if it proceeds fairly, with benefits widespread. But he said it’s too soon to say whether the transition also will bring democracy. “I would say this is a very good opportunity,” Mr. Ojea Quintana said. “But they will need all of the international community to help.”