The party of Burma's democracy icon Aung San Suu Kyi, who spent most of the past two decades under military-ordered house arrest, says she has won a parliamentary seat in historic by-elections.

The Nobel laureate's National League for Democracy party announced the victory shortly after polls closed late Sunday, saying Aung San Suu Kyi won in a rice-farming region south of Rangoon (Kawhmu), soundly defeating two rival candidates.

Her supporters erupted in jubilant cheers as the party announced her win in Rangoon. Despite the NLD celebration, a civil society group monitoring the vote said there were allegations of voting irregularities.

If confirmed, Aung San Suu Kyi's election would mark a major milestone in the Southeast Asian nation, which languished under military rule for nearly half a century until a new nominally civilian government came to power last year and introduced reforms.

U.S. Secretary of State Hillary Clinton, speaking from Istanbul on Sunday, voiced cautious optimism. She said that while the results from Burma's election have not yet been announced, the United States congratulates the people who participated in the campaign and election process.

Suzanne DiMaggio, vice president of global policy programs at the Asia Society, a New York-based non-profit organization, told VOA that although it is clear that the NLD will not hold a majority in the parliament, the symbolism of their win is significant.

The NLD ran candidates in 45 districts, and outcomes elsewhere were not available late Sunday. It was not immediately clear when the government would announce official results.

The NLD won a landslide victory in 1990 general elections, but military leaders at the time refused to relinquish power and the victors were refused entry into parliament.

Voting took place Sunday under the watch of a small group of observers from the European Union and a regional grouping of Southeast Asian nations. However, the monitors were only given a few days to prepare for their mission, and some have said they consider themselves watchers rather than monitors.

U.S. and European Union authorities have hinted that they would consider lifting some economic sanctions imposed on the former military regime, if Sunday's polls are determined to be free and fair. Those sanctions were levied during the past two decades in response to widespread human right abuses under military rule.

The Asia Society's DiMaggio said the U.S. still has reason to be cautious about lifting sanctions on Burma because of the makeup of its military-dominated government. She noted that many of the sanctions are so intricate that it will take time to unpack them. But she said this will provide Washington with an opportunity to test whether the government's reforms are true.