Opposition activists held their second day of protests on Monday against a bid by the central African nation's president to seek a controversial third term in office, witnesses said.

The renewed demonstrations came the day after at least two protestors were shot dead during clashes with police in the capital Bujumbura, and after two further deaths were reported overnight in alleged attacks by ruling party militia.

Unrest erupted on Sunday after the ruling CNDD-FDD party, which has been accused of intimidating opponents for months, designated President Pierre Nkurunziza as its candidate for the June 26 presidential election.

The president has been in power for two terms since 2005, and opposition figures and rights groups say his attempt to stay put goes against the constitution as well as the Arusha peace deal that brought an end to a civil war that killed hundreds of thousands of people.

On Monday demonstrators were back on the streets, with police breaking up a march in Cibitoke, in the north of the capital, of around 1,000 youths trying to reach the centre of the capital.

Several other demonstrations were reported to be taking place across the capital.

The government has banned all protests, and on Sunday halted nationwide broadcasts by Burundi's three main independent radio stations, which have been accused of encouraging an "uprising" against the government.

"The army has been deployed in parts of Bujumbura since last night to maintain public order," Burundian army spokesman General Gaspard Baratuza told AFP, saying the armed forces would not be engaged in anti-riot duties but rather to "protect the population".

Relatives of Sunday's gunshot victims told AFP that they were shot at close range by police.

But speaking on state television, Bujumbura's mayor Saidi Juma claimed the two who died were killed by other demonstrators.

Two further deaths during overnight violence were confirmed by the army.

At least 15,000 Burundians have fled the country to neighbouring Rwanda in recent weeks, according to the UN's refugee agency, which has warned that those numbers could swell.

READ: Crisis looms as Burundians flee to Rwanda

Many are fleeing threats by the pro-government militia Imbonerakure, the youth wing of the ruling CNDD-FDD party. Rights groups allege that the militia has been armed and trained over the past year in order to help Nkurunziza stay in office.

On Saturday, Washington condemned Nkurunziza's candidacy and warned the country was "losing an historic opportunity to strengthen its democracy."

After Sunday's protest deaths, the African Union appealed to Burundi's government to "exercise the highest restraint and protect the population".

The influential Catholic Church has also spoken out against the president's plans to stay put, while UN rights chief Zeid Ra'ad Al Hussein has warned that the country is at a "crossroads" between a fair vote and a route back to its "horrendously violent past".