Protesters opposed to Burundian President Pierre Nkurunziza called for him to step down Tuesday, defying warnings to end weeks of demonstrations as security forces fired shots to restore order after a failed coup.

In one district, civil society leader Dieudonne Bashirahishize led more than a thousand protesters to observe a minute of silence "for the martyrs of the fight for freedom", calling on people to "overcome our fear and continue to demonstrate despite threats".

At least 20 people died in weeks of street battles with security forces before demonstrations ended last week when generals launched a failed coup attempt, but protests resumed again on Monday.

Hundreds gathered in groups in several districts of the capital Bujumbura, dancing and chanting "No to violence!", although others gathered up piles of stones, apparently in case of attack by security forces. Others set up barricades in the streets.

Opposition and rights groups say that Nkurunziza's bid for a third five-year term in power is against the constitution and the terms of the peace deal that brought an end to the country's 13-year civil war in 2006.

"We cannot stop the protests, because President Nkurunziza has not withdrawn his candidacy," said Bernard, a 34-year old unemployed man..

Groups scattered as troops fired warning shots, gathering again elsewhere to resume protest chants. Several protesters were seen who appeared to have been beaten, with swollen or bloody faces.

Mayor Juma Saidi has warned in broadcasts that demonstrators will be "considered as part of the coup", but opposition leader Frederic Banvugiyuvira from the FRODEBU party said protesters "had nothing to do" with it.

"We started before them, and they are now in prison," Banvugiyuvira told the crowds. "We have just shown that Burundians can fight for their rights. We refuse to be slaves of Nkurunziza ... we continue our struggle! If Nkurunziza wants us to leave the streets, he must renounce his third term."

Nkurunziza, a former rebel leader and born-again Christian who believes he has divine backing to lead the country, argues his first term in power did not count as he was elected by parliament, not directly by the people.

He has been accused by rights groups of launching a campaign of repression against opponents and trying to silence independent media since coup leaders admitted defeat on Friday after fierce fighting with loyalist troops.

But the presidency dismissed such claims Tuesday, saying it would never carry out "revenge" raids and promising fair trials for those arrested.

"Those involved in the shameful attempt to overthrow legitimate institutions will be arrested and prosecuted by the courts, and only by them -- and it will be up to them to fix the punishment, as prescribed by law," a statement read.

Almost a week on since the coup attempt led by a top general -- which saw soldiers battling each other on the streets -- troops have largely replaced the police to stem the protests.

But there were also signs of weariness among some protesters, some of whom have been on the streets since late April.

"The people, we're almost dying -- there is no transport, there is no more money," said Deogratias, a 55-year-old artist.

More than 100,000 people have fled to neighbouring nations to escape political violence, according to the UN.

For the first time on Tuesday, foreign journalists were barred from reporting on one area of protests.

Four key private radio stations were attacked and closed during the coup bid, and there is now virtually no independent media in the country, with government broadcasts relaying presidential messages.

Innocent Muhozi, who heads Renaissance television and radio, tried on Tuesday to reopen the station, but was blocked by police. Muhozi called promises of press freedom by the presidency a "joke".