Burma's Aung San Suu Kyi has won a seat in the by-elections for the Parliament, her National League for Democracy party announced.

The Nobel Peace Prize winner, who spent 15 years under house arrest in Myanmar, had won in Kawhmu, south of the commercial capital Yangon.

Even as the opposition National League for Democracy (NLD) claimed a landslide victory in the election, pro-democracy leader Suu Kyi hailed the triumph a ''victory of the people'', the BBC reported.

Official results for the 45 seats that were contested are expected only later this week, but Suu Kyi's party claimed that she had won her Kawhmu constituency. Many of her colleagues have also reportedly won. The Election Commission has not come out without anything so far.

The 66-year-old Nobel peace prize winner Suu Kyi's opponent was a military doctor from the junta-backed Union Solidarity and Development Party (USDP).

Thousands of Suu Kyi's supporters took to the streets of the old capital to celebrate her election victory.

In a statement, she asked her supporters to show restraint in the hour of victory.

''I would like all NLD members to ensure that the victory of the people is a dignified victory," she said, reported the BBC.

"Words, behaviour and actions that ''can harm and sadden other parties and people'' should be avoided, she was quoted as saying.

While US Secretary of State Hillary Clinton congratulated Myanmar on the election, US lawmakers remained cautious; the European Union hinted that it could ease some sanctions. Further moves on this could depend on the post-election developments.

According to Reuters which quoted diplomats, some US curbs such as visa bans and asset freezes could be lifted quickly if the election goes smoothly. The EU may end its ban on investment in timber and the mining of gemstones and metals, the report said.

Other reports said that most of the sanctions could remain in place to force further reforms in the military-ruled country.

For Suu Kyi's National League for Democracy party, this is a defining moment since it won a landslide election victory in 1990. According to AP, the military annulled those results and kept Aung San Suu Kyi in detention for much of the next two decades. The party boycotted the last vote in 2010, but in January the government amended key electoral laws, paving the way for a run in this weekend's ballot, AP added.

Landslide victory for Aung Sang Suu Kyi welcomed IBTimes TV