President Alexander Lukashenko has been declared the overwhelming winner of the election in Belarus, with initial results giving him 82.6% of the vote.
Several thousand Milinkevich supporters rallied in central Minsk
The main opposition candidate Alexander Milinkevich called for a re-run, as thousands of protesters filled a square in Minsk, amid claims of vote-rigging.
A senior European MP called the "whole election a fake". OSCE poll monitors are due to deliver their verdict later.
The US has labelled Mr Lukashenko "Europe's last dictator".
The BBC's Emma Simpson in Minsk says there has been growing concern in Belarus and abroad over how the election has been conducted, and, she adds, the OSCE, Europe's main election-monitoring body, is not expected to mince its words.
Alexander Lukashenko: 82.6%
Alexander Milinkevich: 6.0%
Sergei Gaidukevich: 3.5%
Alexander Kozulin: 2.3%
The opposition are urging their supporters to take to the streets again on Monday evening but it is not clear if President Lukashenko will let them protest for a second night.
There has been no evidence so far of any Ukrainian-style Orange Revolution, our correspondent adds.
About 10,000 people braved a heavy snow storm, freezing temperatures and threat of government reprisals to show their support for the opposition and gather in Oktyabrskaya Square.
They shouted slogans, waved national flags banned under Mr Lukashenko, and booed pictures of the president being shown on a large television screen.
Mr Milinkevich - who received 6% of the vote - told the crowd that claims his rival Mr Lukashenko had won a landslide victory, and thus a third term in office, were a lie.
Lukashenko has vowed to crush any unrest
"We demand new, honest elections. This was a complete farce," he said.
Elmar Brok, the German head of the European Parliament's foreign affairs and human rights committees, also condemned the vote, saying Mr Lukashenko's supporters were sent to control polling stations, and monopolised the media.
"I think this whole election was a fake... I believe that this was this classical type of communist election which we had in the 40s, 50s and 60s in eastern Europe," he told the BBC.
Mr Lukashenko, whose administration has been widely accused in the West of imposing authoritarian rule, has warned he will not tolerate any attempt at a "coup" and has vowed to "break the neck - like a duckling's" of anyone who tries to seize power.
Police have said that protesters "trying to destabilise the situation" will be treated as terrorists and could face the death penalty.
Both the European Union and the US have expressed concern at the Belarussian government's tough stance on political protest.
Dozens of opposition activists were arrested in the run-up to the poll.
Officials in the ex-Soviet republic have accused foreign countries of backing opposition candidates and a number of foreign monitors and journalists were denied entry to watch the vote.
But our correspondent says that despite his authoritarian regime, Mr Lukashenko has genuine popular support, particularly in rural areas.
Many Belarussians credit him with maintaining economic stability and paying pensions on time, and for avoiding the post-communist turmoil seen in neighbouring countries.
Turnout in the election was 92.6%, the Central Election Commission said.