Burma's Nobel laureate Aung San Suu Kyi has won a by-election for parliament, her party says, after a landmark vote which saw 45 seats contested.

Suu Kyi's opposition National League for Democracy (NLD) said she had easily won the vote in Kawhmu, though official counts have not yet finished.

The NLD was competing in its first elections since 1990.

The vote is a key test of promised political reforms, though the military-backed ruling party remains dominant.

During the campaign, foreign journalists and international observers were given the widest access for years.

The European Union hinted that it could ease some sanctions if the vote went smoothly.

"We hope the whole day can be run in a peaceful way and we'll make an evaluation later on the basis of all the polling sessions that we will be seeing," EU observer Ivo Belet said.

The 45 seats under contention are vacancies created by the promotion of parliamentarians to the Cabinet and other posts last year.

Still, the election is an opportunity for voters to weigh in during a time of enormous change in Myanmar, a country also known as Burma.

Aung San Suu Kyi spent much of the last 20 years under house arrest and refused to take part in the 2010 election, which ushered in the current reforms.

The NLD is one of 17 opposition parties taking part in Sunday's election. Only a fraction of seats are up for grabs and the military-backed party will still dominate.

The daughter of Gen. Aung San, a hero of Burmese independence, Suu Kyi herself became an inspiration with her long struggle for democracy in the country.

As a member of parliament, Suu Kyi would be expected to be free to travel outside Myanmar -- and more importantly to return -- something that wasn't possible during her long years of repression and confinement.

She told hundreds of journalists gathered outside her residence Friday that she didn't plan to become a minister in the military-backed civilian government, if a position was offered to her. Under Myanmar's constitution, lawmakers can't hold ministerial office.

Asked where she would place Myanmar's democracy on a scale of one to 10, Suu Kyi said, "We're trying to get to one."