Yangon, Myanmar (CNN) Only a fraction of the results have been announced in Myanmar's historic parliamentary elections, but jubilant crowds still packed the streets outside the headquarters of the main opposition party Monday.

"This is no longer just in our dreams," one man shouted.

A spokesman for Aung San Suu Kyi 's opposition National League for Democracy projected that the party had won 80% of the vote nationwide, based on its unofficial data collated from polling stations across the country.

And the leader of the military-backed ruling party effectively conceded defeat when he said his party had lost more seats than it had won.

"We won in some regions, states and divisions, but also lost in some others," Htay Oo, the Union Solidarity and Development Party's acting chairman, told local TV station DVB. "We have (a) higher percentage of losses than wins." He himself had failed to win his seat, he said.

In early results from Sunday's vote -- billed as the country's freest in a generation -- the National League for Democracy had won 78 of 88 seats declared so far in the lower house of parliament. Hundreds more results, including many from remote areas with poor infrastructure, need to be announced before the full picture becomes clear.

The ruling party of President Thein Sein -- a former general who has overseen a series of political reforms in recent years -- had won only five of the seats declared so far, election officials said.

Jubilant scenes

NLD supporters gathered amid jubilant scenes outside the party's Yangon headquarters Monday night, in anticipation of a historic, landslide victory in Myanmar , which is also known as Burma.

Music played as they waved flags bearing the NLD's golden peacock emblem; many wore T-shirts emblazoned with pictures of Suu Kyi.

"We believe we can win," Ayea Nyeian Thu, a doctor, told CNN at the rally. "We don't want to see a military government any longer."

JUST WATCHED Why the stakes are so high for Aung San Suu Kyi's NLD Replay More Videos ... MUST WATCH Why the stakes are so high for Aung San Suu Kyi's NLD 06:12

NLD supporters had been waiting a long time for a democratic vote, she said. "We want to celebrate."

The landmark election is seen as a test of the powerful Myanmar military's willingness to let the country continue along a path toward full democracy, after decades of military-dominated rule.

Thein Sein has promised that the outcome of Sunday's vote will be respected, but the system is already configured strongly in favor of the military, which gets to appoint a quarter of all lawmakers in the two houses of parliament.

That means the NLD would need to win more than two-thirds of the remaining seats in each house to secure majorities.

The public is electing 168 of the 224 representatives in the upper house of the national parliament, with the remaining quarter of seats reserved for lawmakers appointed by the military.

In the lower house, 325 of the 440 seats are up for grabs. Another 110 are reserved for military appointees, while voting has reportedly been canceled in the remaining five electable lower house seats because of security concerns.

Free and fair?

Photos: Landmark elections in Myanmar A woman casts her vote in a polling station in Naypyidaw, Myanmar, on Sunday, November 8. Hide Caption 1 of 10 Photos: Landmark elections in Myanmar A woman's finger is dipped in ink after casting her ballot in Dala, a village outside of Yangon, Myanmar, on November 8. Hide Caption 2 of 10 Photos: Landmark elections in Myanmar People rally outside the National League for Democracy office after Myanmar's first free and fair election in 25 years on November 8 in Yangon. Hide Caption 3 of 10 Photos: Landmark elections in Myanmar Votes are counted in a polling station in Yangon on November 8. Hide Caption 4 of 10 Photos: Landmark elections in Myanmar A vendor reads a local weekly journal showing a portrait of Myanmar opposition leader Aung San Suu Kyi, President Thein Sein and others. Hide Caption 5 of 10 Photos: Landmark elections in Myanmar Pro-democracy supporters are optimistic that the election could be the beginning of real change in the country, which has been isolated for decades because of its repressive military-dominated government. Hide Caption 6 of 10 Photos: Landmark elections in Myanmar Tin Aye, chairman of Myanmar's Union Election Commission, inspects a polling station in Naypyidaw on November 7. Hide Caption 7 of 10 Photos: Landmark elections in Myanmar Thu Ryain Shwe, 26, of the National Unity Party, one of the youngest candidates in the parliamentary election, wears his candidate ID in Zigon. Hide Caption 8 of 10 Photos: Landmark elections in Myanmar A devotee prays at a chanting ceremony in Mandalay, Myanmar, on November 7 to bless citizens and to pray for a fair and peaceful election. Hide Caption 9 of 10 Photos: Landmark elections in Myanmar A supporter of Aung San Suu Kyi's National League for Democracy party holds a party flag in Mandalay on November 5. Hide Caption 10 of 10

The changes ushered in under Thein Sein since 2011 have helped reduce the country's international isolation, with Western sanctions being eased and foreign investment starting to ramp up.

But human rights groups have warned more recently of a rise in politically motivated arrests as well as discrimination directed against the Muslim minority, notably the stateless Rohingya population

JUST WATCHED Who is Aung San Suu Kyi? Replay More Videos ... MUST WATCH Who is Aung San Suu Kyi? 02:24

Questions have come up over how free and fair the current election will turn out to be. Suu Kyi, a Nobel Peace Prize laureate, expressed concern last week about irregularities in advance voting, fraud and intimidation.

Many people still remember the last national election her party contested, in 1990, which it was widely considered to have won. But the military rulers annulled the results and placed Suu Kyi and many of her colleagues under arrest.

Suu Kyi, the daughter of an independence leader, spent much of the next two decades under house arrest, becoming an internationally recognized symbol of democracy and the country's most popular politician.

'More openness and transparency'

Some observers have questioned the impartiality of the Union Election Commission, the body that oversees the vote, which has ties to the ruling USDP.

JUST WATCHED Vote count under way in Myanmar's landmark election Replay More Videos ... MUST WATCH Vote count under way in Myanmar's landmark election 02:10

Daw Thein Thein Tun, an official from the commission, insisted Sunday that this election was much better than parliamentary elections in 2010, which were boycotted by the NLD.

"There are more people this time compared to 2010," she told CNN.

"There is more regulation, and this time there is more openness and transparency," she added. "You see the voting is free and fair."

But NLD candidate Nay Phone Latt was skeptical. He told CNN that the party had monitored some irregularities and had noted minor incidents of violence and attempted voter fraud.

He added that the likelihood of foul play would be strongest in remote rural areas.

Hundreds of thousands of people in Myanmar are disenfranchised, including Rohingya Muslims in the west of the country, who are denied citizenship, and residents of conflict zones where the election commission canceled voting.

Suu Kyi barred from presidency

After the outcome of the parliamentary vote is decided, lawmakers will begin the complex process of choosing a president.

Suu Kyi, who was elected to parliament in a by-election in 2012 and is seeking re-election for her seat this year, is barred from the presidency by the military-drafted constitution, which prohibits anyone with foreign family members from assuming the top office. Suu Kyi's late husband was British, and her two sons have British passports.

Suu Kyi said last week she would be "above the President" if her party won the parliamentary election.

Photos: Photos: Suu Kyi through the years Aung San Suu Kyi, the Burmese opposition politician and Nobel Peace Prize winner, arrives at the polling station to cast vote during Myanmar's freest election in decades on November 8, 2015. Known worldwide for her leadership and commitment to human rights in Myanmar, she was kept under house arrest for years by the Asian country's military rulers. Take a look back at her triumphs and struggles: Hide Caption 1 of 24 Photos: Photos: Suu Kyi through the years Suu Kyi through the years – Suu Kyi, center, receives the U.S. Congressional Gold Medal on September 19, 2015. She is flanked by (from left) House Speaker John Boehner, House Minority Leader Nancy Pelosi, Secretary of State Hillary Clinton and Senate Minority Leader Mitch McConnell, stand with her. Hide Caption 2 of 24 Photos: Photos: Suu Kyi through the years Suu Kyi through the years – A large cutout of the Congressional Gold Medal awarded to Suu Kyi is on display on Wednesday. Hide Caption 3 of 24 Photos: Photos: Suu Kyi through the years Suu Kyi through the years – Suu Kyi meets with Secretary of State Hillary Clinton on Tuesday, September 18, in Clinton's office at the State Department in Washington. It was her first visit to the U.S. in 20 years. Hide Caption 4 of 24 Photos: Photos: Suu Kyi through the years Suu Kyi through the years – Suu Kyi greets her supporters as she visits a recently flooded area in Pathein township, the capital city of the Irrawaddy division, on September 1, 2015. Heavy monsoon rains in Myanmar forced tens of thousands of people to seek shelter in emergency camps. Hide Caption 5 of 24 Photos: Photos: Suu Kyi through the years Suu Kyi through the years – Suu Kyi speaks during a regular session at the lower house of parliament in Naypyidaw, Myanmar, on July 25, 2015. Suu Kyi called for laws to protect the rights of the nation's myriad ethnic minorities in her inaugural address to the fledgling parliament. Hide Caption 6 of 24 Photos: Photos: Suu Kyi through the years Suu Kyi through the years – Suu Kyi sits in the lower house parliament session in Naypyidaw on July 10, 2015. Hide Caption 7 of 24 Photos: Photos: Suu Kyi through the years Suu Kyi through the years – Suu Kyi prays in honor of her late father, independence hero Gen. Aung San, during a ceremony to mark the country's 65th anniversary of Martyrs' Day at the Martyrs' Mausoleum in Yangon, Myanmar, on July 19, 2015. The memorial is a tribute to Aung San and several other independence leaders who were killed on July 19, 1947. Hide Caption 8 of 24 Photos: Photos: Suu Kyi through the years Suu Kyi through the years – Suu Kyi stands to address both houses of Parliament in Westminster Hall, London, on June 21, 2015 as Speaker of the House of Commons John Bercow, right, and Speaker of the House of Lords Baroness D'Souza stand beside her. Suu Kyi made a historic address to both houses of the British Parliament, making her only the fifth foreign dignitary since World War II to be accorded the rare honor. Hide Caption 9 of 24 Photos: Photos: Suu Kyi through the years Suu Kyi through the years – Suu Kyi speaks during a Nobel lecture at Oslo City Hall on June 16, 2015 in Oslo, Norway. She was awarded the Nobel Peace Price in 1991 but had not been able to receive it until now because she was kept under house arrest for most of the past 24 years. Hide Caption 10 of 24 Photos: Photos: Suu Kyi through the years Suu Kyi through the years – Suu Kyi visits the Mae La refugee camp on June 2, 2015 in the western province of Tak, Thailand. The camp, situated along the Myanmar-Thailand border, is home to around 45,000 Karen people, an ethnic minority in Myanmar. Hide Caption 11 of 24 Photos: Photos: Suu Kyi through the years Suu Kyi through the years – Suu Kyi leaves the Suvarnabhumi International airport on her first international trip in 24 years outside Myanmar on May 29, 2015in Bangkok, Thailand. Hide Caption 12 of 24 Photos: Photos: Suu Kyi through the years Suu Kyi through the years – Suu Kyi waves to Burmese workers on a trip to a migrant community outside of Bangkok on May 30, 2015 in Samut Sakhon, Thailand. Suu Kyi pledged to help improve the rights of Burmese nationals living in Thailand. Hide Caption 13 of 24 Photos: Photos: Suu Kyi through the years Suu Kyi through the years – Suu Kyi speaks at the National League for Democracy party headquarters after after a landslide victory for a seat in the parliament on April 2, 2015 in Yangon. The NLD claimed 43 out of 44 parliamentary seats as the country continues its path of political and diplomatic reform. Hide Caption 14 of 24 Photos: Photos: Suu Kyi through the years Suu Kyi through the years – Suu Kyi is surrounded by media as she visits polling stations in her constituency during the parliamentary elections on April 1, 2015 in Kaw Hmu, Myanmar. Hide Caption 15 of 24 Photos: Photos: Suu Kyi through the years Suu Kyi through the years – Suu Kyi and Secreatary of State Hillary Clinton stand together during a news conference after their meeting at her residence in Yangon on December 2, 2011, where they laid out a framework for reforms. Hide Caption 16 of 24 Photos: Photos: Suu Kyi through the years Suu Kyi through the years – Suu Kyi speaks in Yangon during a meeting to mark Human RIghts Day on December 10, 2010. Hide Caption 17 of 24 Photos: Photos: Suu Kyi through the years Suu Kyi through the years – Suu Kyi addresses thousands of her supporters at her National League for Democracy headquarters on November 14, 2010. Hide Caption 18 of 24 Photos: Photos: Suu Kyi through the years Suu Kyi through the years – Suu Kyi greets crowds of well-wishers at the gate of her house after her release from house arrest, on November 13, 2010, in Yangon. Hide Caption 19 of 24 Photos: Photos: Suu Kyi through the years Suu Kyi through the years – U.S. President George W. Bush signs H.R. 4286, which gave the Congressional Gold Medal in absentia to Suu Kyi, in the Oval Office of the White House on May 6, 2008. From left : California Sen. Dianne Feinstein, U.S. Rep. Joe Crowley of New York, first lady Laura Bush and Kentucky Sen. Mitch McConnell. Hide Caption 20 of 24 Photos: Photos: Suu Kyi through the years Suu Kyi through the years – Suu Kyi listens to a question during a news conference after being freed from 19 months under house arrest May 6, 2002, making a triumphant return to her party's headquarters in Yangon. A year later, her motorcade was attacked by a pro-government mob, and she was placed under house arrest again. Hide Caption 21 of 24 Photos: Photos: Suu Kyi through the years Suu Kyi through the years – Suu Kyi's son, Alexander Aris, left, accepts America's highest civilian honor from U.S. President Bill Clinton on his mother's behalf on December 6, 2000, at the Eisenhower Executive Office Building in Washington. Hide Caption 22 of 24 Photos: Photos: Suu Kyi through the years Suu Kyi through the years – Suu Kyi addresses hundreds of anxious Burmese supporters from the main gate of her family compound in Yangon on July 14, 1995. Hide Caption 23 of 24 Photos: Photos: Suu Kyi through the years Suu Kyi through the years – Suu Kyi speaks in Yangon during an anti-military regime rally on August 26, 1988. Hide Caption 24 of 24

Complicating any efforts to change the rules in the future, the military also has an effective veto over any proposed constitutional changes.

In spite of the political maneuvering that may lie ahead, U.S. Secretary of State John Kerry congratulated the country on holding the election Sunday.

"Millions of people from around the country, many of whom were voting for the first time, seized this opportunity to move one step closer to a democracy that respects the rights of all -- a testament to the courage and sacrifice shown by the people of Myanmar over many decades," he said in a statement.

But Kerry added that the election was "far from perfect," noting "important structural and systemic impediments to the realization of full democratic and civilian government."