Opposition leader Aung San Suu Kyi arrives at a polling station to cast her vote during Burma’s election. (Lam Yik Fei/Getty Images)

The day after millions in Burma voted peacefully in the country’s first democratic election in years, opposition leader Aung San Suu Kyi’s party confidently projected victory even as results began trickling in.

Suu Kyi, 70, whose long battle for democracy in Burma made her an international human rights icon, appeared at the National League for Democracy headquarters in Rangoon Monday, saying it was “too early” to start congratulating winners.

But, she added, “I think you all have an idea of the results.”

Suu Kyi also warned her supporters not to “provoke” the losers in the pitched election battle, where her party appears to be edging toward victory over the military-backed Union Solidarity and Development Party.

Millions of the country’s 30 million voters had braved hot sun and long lines to cast their ballots in the historic election Sunday, the first national democratic vote in 25 years.

More than 10,000 election observers were on hand to make sure the process went smoothly, but concerns rose Monday over claims that a number of ballots flowed in late that tipped the balance for the military-backed USDP in some races in further-flung states.

“People stood hours in line in the sun and celebrated yesterday and today there is a huge disappointment because their vote didn’t count,” said Meenakshi Ganguly of Human Rights Watch, who observed voting in Kachin state.

Hundreds of supporters of the NLD remained on the street after voting in front of the party headquarters, waving red balloons, dancing, and celebrating. They watched the preliminary vote counting on big-screen TVs until late in the night, cheering every time a yellow ballot was unfurled with a stamp next to a golden peacock, the symbol for the NLD.

“We have been suffering for 25 years. Today, we change the old system and bring in a new one,” Theingi, a homemaker and mother of two, said. She uses only one name.

Suu Kyi’s party leaders predicted huge victory margins at the polls in the Southeast Asian nation of 51 million, which was isolated from the world for more than a half century under a military dictatorship.

But the path to victory is hardly clear. Party members appear to be confident they will get the majority needed to govern. But the military will still control 25 percent of the seats in parliament and key ministries. A constitutional provision bars Suu Kyi, called “Mother Suu,” from becoming president. And Burma, also known as Myanmar, has more than 90 parties — smaller groups that support Burma’s ethnic minorities — that will also play a factor in forming a new government.

Suu Kyi had said earlier in the week that if her party wins the majority of seats in parliament, she will govern the country despite the constitutional barrier.

“I’m going to be above the president,” she said. When asked how, she responded, “Oh, I have already made plans.”

The country’s president Thein Sein, a former general, said Friday that the government would respect the outcome of the election, and many voters seemed eager to take him at his word.

In Burma’s last democratic election in 1990, Suu Kyi and the NLD won an overwhelming majority, but the country’s military dictators ignored the results. They had in 1989 placed her under house arrest, where she remained off and on for nearly two decades.

“I think it will be free and fair overall,” said one of Sein’s supporters, Aye Aye Mu, 28, a mother of two who comes from a military family.

Critics have said that these elections cannot be considered truly free because voting was not held in some areas of the country still fraught with ethnic violence. And about 1 million Rohingya Muslims, who are stateless and considered by the government to be illegal immigrants from neighboring Bangladesh, have been stripped of their right to vote.

More than 100,000 Rohingya still reside in displacement camps after Muslim and Buddhist violence in 2012.

“We’ve said it is difficult to see how this can be a truly free and fair election given the disenfranchisement of the Rohingya population, the 25 percent of parliament guaranteed to the military and other structural problems,” said Tom Malinowski, assistant U.S. secretary of state for democracy, human rights and labor. “But there can still be a result that credibly reflects the overall desires of a majority of the Burmese people.”

The election is being closely watched by Burma’s supporters in the West, particularly in the Obama administration, which encouraged the regime’s shift toward democracy by easing sanctions and sending nearly $500 million in aid.

In a statement, Secretary of State John F. Kerry commended the nation on a “peaceful and historic poll” in which millions voted for the first time.

“While these elections were an important step forward,” he said, “we recognize that they were far from perfect. There remain important structural and systemic impediments to the realization of full democratic and civilian government, including the reservation of a large number of unelected seats for the military; the disfranchisement of groups of people who voted in previous elections, including the Rohingya; and the disqualification of candidates based on arbitrary application of citizenship and residency requirements.”

Officials have expressed concern that Burma’s reforms could be stalling, and dismay over a series of tough new laws governing family size, religious conversion and interfaith marriage, seen as targeting the country’s Muslim minority.

More than 30 million voters were eligible to cast ballots for the upper and lower houses of parliament, as well as state and regional assemblies.

The country’s new computerized voter-registration rolls have been widely criticized for repeating and skipping names, but the Carter Center said in a report Oct. 27 that many specific claims of errors appeared to be “unsubstantiated.”

Outside Rangoon, the busy streets give way to flat farmland, dotted with simple huts with woven bamboo walls, mango groves and palm trees. Residents there — among the 70 percent of the population who still eke out a living in agriculture — said they were more concerned about their livelihoods of river fishing and farming than politics, and that their local candidates had never come to see them. One village received electricity only four months ago.

Nevertheless, on Sunday there were lines to get into the polling station in a school compound — men in one building, women in the other. Banners on the wall demonstrated voting procedures in graphics for those who had never voted before. A poll worker told the women that if they needed to go home to cook for their families, they could come back later before polls closed at 4 p.m.

Latt Latt Win, 34, clutched her 1-year-old daughter and said she had risen at 6 a.m. at her bean farm and traveled by boat, then precarious motorbike, to reach her polling place. She had been spurred to make the two-hour journey by all the media coverage, she said, and she thought it was her responsibility.

“I wanted to vote,” she said. “I got up, said my morning prayer and came here.” But she had still not made up her mind about her vote.

Sein Kyaw Thee, 45, who makes about $15 a day as a fisherman, said he voted for Suu Kyi’s party because he hoped it would bring prosperity to Burma and because he reveres her.

“The party is like the parents of the public,” he said. “But it’s not because of the party, it’s because of Mother Suu.”

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Today's coverage from Post correspondents around the world