Western powers have dismissed Burma's first general election for two decades, describing it as neither free nor fair.
US President Barack Obama said Sunday's poll had not met "internationally accepted standards". EU governments have also criticised the election.
Early official results show successes for parties linked to the military. The main opposition NLD boycotted the vote.
Meanwhile, deadly clashes near the Thai border sparked fears the poll could re-ignite conflicts with ethnic militias.
Three people were reported killed in or near the town of Myawaddy, where a Karen rebel faction was reported to be clashing with government troops. There were also reports of grenade fire over the border into Thailand.
A Japanese journalist was reportedly being held in Myawaddy on suspicion of illegal entry. Foreign journalists and monitors have not been allowed into Burma.
In a joint statement, the US and Australia criticised the polls and called for the immediate release of Aung San Suu Kyi and other political prisoners.
"Australia and the United States underlined their deep regret that the Burmese authorities failed to hold free, fair and genuinely inclusive elections," said the statement issued by US Secretary of State Hillary Clinton and Defence Secretary Robert Gates after talks with Australian Foreign Minister Kevin Rudd and Defence Minister Stephen Smith in Melbourne.
The statement urged the government to ensure that post-election institutions were "transparent, accountable and responsive to their citizens' aspirations".
Some voters told the BBC they could not vote in private, while opposition groups alleged that many state employees had been pressured to vote in advance for the main pro-military party.
Reports from Burma's largest city, Rangoon, suggest turnout was low.
Burmese voters last got a chance to cast their ballots in 1990, when they overwhelmingly backed the National League for Democracy (NLD) led by Aung San Suu Kyi.
But the ruling generals never allowed the NLD to take power and detained Ms Suu Kyi.
A new constitution enacted in 2008. The election was the culmination of the generals' stated aim to create a "discipline-flourishing democracy" that will return Burma to civilian rule. However, critics say they are a sham.
A quarter of seats in the two new chambers of parliament will be reserved for the military.
Any constitutional change will require a parliamentary majority of more than 75% - meaning that the military will retain a casting vote. Key ministerial posts will be held by serving generals.
The two main parties contesting the polls - the Union Solidarity and Development Party (USDP) and the National Unity Party (NUP) - also have close ties to the military, with both led by former generals who have given up their ranks.
The NLD was forcibly disbanded after it said it was not participating because of laws which banned Ms Suu Kyi from taking part.
President Obama, speaking on Sunday during a visit to India, said the elections would "be anything but free and fair".
"For too long the people of Burma have been denied the right to determine their own destiny."
In a statement released by the White House afterwards, Mr Obama said the vote had not met "any of the internationally accepted standards associated with legitimate elections", and called for the immediate release of Ms Suu Kyi and all other political prisoners in Burma.
The UK said the election results were "already a foregone conclusion".
"Holding flawed elections does not represent progress," Mr Hague said. "For the people of Burma, it will mean the return to power of a brutal regime that has pillaged the nation's resources and overseen widespread human rights abuses."
France urged the Burmese authorities to "sincerely commit to the path of dialogue with the whole of the opposition, and with minorities".
The EU's foreign policy chief, Catherine Ashton, also called on the military "to ensure these elections mark the start of a more inclusive phase".
The president of the opposition Shan National Democratic Party, which is fielding the fourth largest number of candidates, complained that "the authorities of various levels forced the people to cast advance votes".
"We are not allowed to send representatives to the polling stations," Sai Ai Pa O said. "If the election was free and fair, I am sure we would win at least 80% of seats."
Opposition candidates have struggled to fund their campaigns and have complained of harassment.
One soldier based near Rangoon told the BBC that rank-and-file troops from 10 army regiments had refused orders to vote. His testimony could not be verified.
Burma has been hit in recent days by major internet disruption, which some believe is an attempt by the junta to restrict communications over the poll period.