Burma's pro-democracy leader Aung San Suu Kyi hailed a ''victory of the people'' following a declaration by her party that she has won a seat in parliament.
Official results for the by-election on Sunday that saw 45 seats contested are expected later this week.
But Ms Suu Kyi's opposition National League for Democracy (NLD) said she had easily won in her Kawhmu constituency.
In a statement, she urged supporters to show restraint in their celebrations.
''I would like all NLD members to ensure that the victory of the people is a dignified victory," she said in the statement late on Sunday.
Words, behaviour and actions that ''can harm and sadden other parties and people'' should be avoided, she said.
Thousands of people who gathered outside the NLD headquarters in Rangoon danced and cheered at reports that Ms Suu Kyi had won her seat.
"It is the people's victory! We have taught them a lesson," one shopkeeper wearing an NLD T-shirt told the Associated Press news agency.
The vote is a key test of political reforms, though the army and its allies dominate the 664-seat parliament.
The NLD was competing in its first elections since 1990. It was one of 17 opposition parties that took part in Sunday's election.
Apart from winning her own seat, Ms Suu Kyi appears to have helped a number of her colleagues to victory, correspondents say.
NLD officials say they believe the party has won many seats - but there has been no formal word yet from the Election Commission.
Even if the NLD wins most of the seats, the army and its proxy Union Solidarity and Development Party (USDP) will still hold about 80% of seats in parliament.
Ms Suu Kyi - who spent years under house arrest after her party won polls in 1990 but was not allowed to take power - has promised to use her voice to continue to push for further reform.
During the campaign, foreign journalists and international observers were given the widest access to the former military-ruled nation for years.
US Secretary of State Hillary Clinton congratulated Burma on holding the vote and said that the US was ''committed to supporting these reform efforts".
The European Union hinted that it could ease some sanctions if the vote went smoothly.
US lawmakers who drafted sanctions against Burma remained cautiously optimistic.
"While much remains to be done in Burma, Suu Kyi's apparent election to parliament, like that of the apparent election of large numbers of her NLD colleagues, is an important step forward for the country," said Senator Mitch McConnell.
Representative Joe Crowley said ''now is not the time'' to rush towards lifting the sanctions.
"Far too many political prisoners are still locked behind bars, violence continues against ethnic minorities and the military dominates not only the composition but the structure of the government," he added.