Burma's main military-backed political party says it won about 80% of votes in the first election in 20 years.
A Union Solidarity and Development Party (USDP) official said the party was pleased with the result.
The main pro-democracy party, the NLD, boycotted the poll but other opposition groups have alleged widespread fraud.
Meanwhile, fighting between ethnic Karen rebels and government forces sparked by the poll has caused at least 15,000 people to flee into Thailand.
Refugee officials are scrambling to provide shelter for the huge influx of Burmese near the Thai border town of Mae Sot.
Residents in the town of Myawaddy said Burmese troops have now pushed back ethnic Karen rebels, who stormed government buildings on Sunday to protest against the election.
A faction of the Democratic Karen Buddhist Army (DKBA) occupied a police station and polling booth in a show of opposition to the government's plan to incorporate ethnic armies into a centrally-controlled border force.
Burmese troops are reportedly trying to dislodge ethnic Karen fighters from around the Three Pagodas Pass, which lies further south.
'Victory'
It remains unclear when any official result will be announced.
The poll is the first in Burma since 1990, when Aung San Suu Kyi's NLD party secured an overwhelming victory but was never allowed to take power.
The junta says the election marks the transition from military rule to a civilian democracy, but the poll has been widely condemned as a sham. Western governments say it was neither free nor fair.
UN Secretary General Ban Ki-moon has described it as insufficiently inclusive and transparent.
Despite this, some analysts say the election - although deeply flawed - could mark the start of a process of democratisation, by giving opposition lawmakers a voice, however limited, in the institutional decision-making process.
In Burma, pro-democracy opposition groups have made claims of fraud in the counting of votes in Sunday's election.
Formal protests have been lodged with the Election Commission by at least six political parties.
These focus on the practice of advance voting, in which the government escorted government workers - civil servants and soldiers - to polling booths in the days before the poll.
"We took the lead at the beginning but the USDP later came up with so-called advance votes and that changed the results completely, so we lost," Khin Maung Swe, leader of the National Democratic Force, the largest opposition party, told Reuters.
Other opposition figures earlier told BBC Burmese that while they had won at the polling stations - where a first count of ballots was sealed - they later lost at the Commission.
Voters were electing candidates to a two-chamber parliament and 14 regional assemblies.
More than two-thirds of the 3,000 candidates were running for two parties closely linked to the military junta.
The USDP is closely aligned with the head of the Burmese military government, Gen Than Shwe.
Dozens of senior officers have recently "retired" to stand for the party.
The constitution, which was written by the ruling generals, reserves more than a quarter of seats in the new parliament for the army.
The combined force of these two groups will likely mean that they have an effective veto over legislation.
More than 2,000 political prisoners were unable to take part.
