Updated 11:21 a.m. ET: Aung San Suu Kyi claimed victory Monday in Myanmar's historic by-election, saying she hoped it would mark the beginning of "a new era" for the long-repressed country.

Suu Kyi spoke to thousands of cheering supporters who gathered outside her opposition party headquarters a day after her party declared she had won a parliamentary seat in the closely watched vote.

The Election Commission has not yet confirmed the results, but government officials have commented on Suu Kyi's victory and the people of Myanmar, also known as Burma, have reacted with jubilation.

"The success we are having is the success of the people," Suu Kyi said, as a sea of supporters chanted her name and thrust their hands into the air to flash "V" for victory signs.

In Myanmar, Suu Kyi wins parliament seat, raises hopes for democracy

"It is not so much our triumph as a triumph of the people who have decided that they have to be involved in the political process in this country," she said. "We hope this will be the beginning of a new era."

If confirmed, Suu Kyi will take public office for the first time and lead a small bloc of lawmakers from her opposition National League for Democracy in Myanmar's military-dominated Parliament.

The victory would mark a major milestone in the Southeast Asian nation, which is emerging from a ruthless era of military rule, and also an astonishing reversal of fortune for a woman who became one of the world's most prominent prisoners of conscience.

Suu Kyi wins seat in historic Myanmar election

The U.S. on Monday hailed the result as an important step in the country's "democratic transformation".

"We hope it is an indication that the government of Burma intends to continue along the path of greater openness, transparency, and reform,'' Jay Carney, press secretary for U.S. President Barack Obama, said in a statement.

The United States and European Union had hinted they could lift some sanctions - imposed over the past two decades in response to human rights abuses - if the election were free and fair.

Nay Zin Latt, an adviser to President Thein Sein, told The Associated Press he was "not really surprised that the NLD had won a majority of seats" in the by-election.

Party wins 43 out of 45 seats
Asked if Suu might be given a Cabinet post, he said: "Everything is possible. She could be given any position of responsibility because of her capacity."

Unofficial counts continued to trickle in Monday from poll watchers within Suu Kyi's party, and spokesman Han Than said the opposition had won at least 43 of the 44 parliament seats it had contested. Those included all four seats up for grabs in the capital, Naypyitaw, which is populated by civil servants and would be an embarrassing sign of defeat for the government.

The NLD did not contest one of the 45 by-elections.

Khin Maung Win / AP

Myanmar pro-democracy leader Aung San Suu Kyi talks to supporters at the headquarters of her National League for Democracy party in Yangon, Myanmar Monday.

Suu Kyi had complained last week of "irregularities", though none seemed significant enough to question the vote.

Voters had filed into makeshift polling stations from dawn on Sunday, some gushing with excitement after casting ballots for the frail-looking Suu Kyi, or "Aunty Suu" as she is affectionately known.

Among supporters who voted in her rustic constituency of bamboo-thatched homes in Kawhmu, there was little doubt she would win.

"Almost everyone we asked voted for Aunty Suu," Ko Myint Aung, a 27-year-old shop owner told Reuters.

The Associated Press and Reuters contributed to this report.

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