Myanmar opposition leader Aung San Suu Kyi and her National League for Democracy (NLD) won Sunday's election, the co-chairman of the military-backed ruling party announced, potentially paving the way for the country's first popularly-elected government in half a century.

"We lost," Reuters reported Htay Oo of the Union Solidarity and Development Party as saying. "We have to find out the reason why we lost. However, we do accept the results without any reservations."

Htay Oo lost his seat in parliament. Also conceding his seat was parliament speaker Shwe Mann. An NLD spokesman said the party had won 70 percent of the vote, according to the Associated Press. Military commander-in-chief Min Aung Hlaing said there was "no reason not to accept the election results," the Guardian reported, citing state media.

Suu Kyi struck a confident, conciliatory tone Monday, after an election that observers said was very peaceful and orderly.

“It is still a bit early to congratulate our candidates who will be the winners,” the Guardian reported Suu Kyi telling supporters at NLD headquarters in Yangon. “I want to remind you all that even candidates who didn’t win have to accept the winners, but it is important not to provoke the candidates who didn’t win to make them feel bad.”

She won the 1990 election but the military, which has ruled since 1962, refused to hand over power and put her under house arrest for most of the next 20 years. 

On Sunday, about 70 percent to 80 percent of more than 30 million eligible voters cast ballots, media reports said. And one election observer said he visited 14 voting centers and cited just a few issues, all of which were resolved without incident.

“The elections exceeded my expectations," Myanmar Times reported Damaso Magbual, head of mission of Asian Network for Free Elections, as saying.

The Union Election Commission will hold a press conference and release partial results Monday, before releasing final results tomorrow, the Guardian said.

Suu Kyi needs to take two-thirds of all contested seats to gain a majority because the military gets to fill a quarter of all seats. She also cannot be elected president by the parliament, because of a law that bars people with foreign spouses and relatives. Her late husband and their two sons are British. Last week, she said if the NLD won a majority, she would rule as party leader "above" the country's president. Parliament will only elect a new president in February.