Officials in Uganda, Tanzania and Rwanda yet to publicly comment on the latest unrest.
In Nairobi, Foreign Affairs Permanent Secretary Karanja Kibichio told Nation FM on Monday evening that he would travel to Burundi on Friday to donate 150 laptops to the Election Commission but refused to be drawn into the third-term debate.
Six people have been killed since protests broke out on Sunday.
East African Community governments remained quiet Tuesday as protestors opposed to President Pierre Nkurunziza's bid for a third term in office clashed with police for the third day in Burundi, and as the unrest spread to other parts of the country.
Pierre Claver Mbonimpa, a leading human rights activist arrested on Monday, was released without charge on Tuesday evening as international pressure grew on authorities in Burundi to allow peaceful protests.
Officials in Uganda, Tanzania and Rwanda were yet to publicly comment on the latest unrest in Burundi, despite the number of civilians fleeing the EAC member state rising to over 20,000.
In Nairobi, Foreign Affairs Permanent Secretary Karanja Kibichio told Nation FM on Monday evening that he would travel to Burundi on Friday to donate 150 laptops to the Election Commission but refused to be drawn into the third-term debate.
"As a friendly country, our role is to support the decision of the people of Burundi," he said. "Our role is not to interrogate whether decisions are constitutional or not."
In Gitenga, Burundi's second largest city located 100 kilometres east of the capital Bujumbura, police fired tear gas and stopped a planned march by students and other residents in the country's worst spell of instability since the end of the civil war in 2005.
Violate constitution
UN Secretary-General Ban Ki-moon on Tuesday called for an investigation into the killings of protestors and said he was sending his Special Envoy for the Great Lakes Region, Said Djinnit, to Bujumbura to meet President Nkurunziza and other government officials in an attempt to defuse the crisis.
Shots could be heard in the capital and several suburbs as police battled to remove burning barricades strewn across streets leading into the city centre.
Six people have been killed since the protests broke out on Sunday, a day after the CNDD-FDD, the ruling party, nominated Mr Nkurunziza as its candidate for the June 26 election.
Opposition supporters as well as political and civil society activists say a third term would violate the country's constitution and the terms of the Arusha Agreement signed to end a decade of civil war in which about 130,000 people were killed.
Mr Nkurunziza's supporters say his first term, between 2005 and 2010, does not count because he was elected by legislators and not directly by the population. The government has described the protestors as an "insurrectional movement", shut down independent radio stations and arrested hundreds of people.
"Despite the arrests, we will continue," Vital Nshimirimana, a political activist who has gone into hiding to avoid arrest, told Radio France International by telephone. He said the protests would continue until President Nkurunziza renounces his claim for a third term in office.
US government officials have publicly asked President Nkurunziza not to seek re-election and the US embassy in Bujumbura said it was watching the situation closely and would "hold accountable those responsible for violence against the civilian population".
In a message on its Twitter account on Sunday, the British High Commission in Rwanda said London "deeply regrets" the decision to nominate Mr Nkurunziza for re-election.
The European Union also issued a statement on Tuesday calling for calm and warning that the violence, arrests of human rights activists and clampdown on the media would undermine the credibility of the electoral process.
African Union chairperson Nkosazana Dlamini-Zuma has also publicly raised concerns about the political situation in Burundi and the AU Peace and Security Council was meeting on Tuesday afternoon to discuss the situation in the country.
Burundians in the diaspora also held small, peaceful protests in Belgium and the Netherlands.
Delicate balance
An estimated 15,000 people have fled the violence, going mostly into Rwanda, according the UN High Commissioner for Refugees, amidst fears that the conflict could spill over into the Great Lakes region and take on ethnic dimensions.
The Arusha Agreement and Burundi's constitution specify a delicate power-sharing framework in the country, which has a Hutu majority and a Tutsi minority with a much smaller number of BaTwa people.
President Nkurunziza is a former leader of a Hutu rebel group, as is his main political challenger, Agathon Rwasa. Both the government and the main opposition parties are political alliances across ethnicities but there are fears that the current instability could unravel the delicate bridges built over the ethnic divide.
Former President Pierre Buyoya, who led the country between 1987 and 1993, and between 1996 to 2003, has warned that the country could slide back to civil war if the crisis is not resolved quickly.
The vice president of the ruling CNDD-FDD party on Tuesday compared RPA, the popular radio station shut down on Monday for reporting about the protests, to Radio Mille Collines, accused of fanning the 1994 genocide in Rwanda.
Rwanda has thrown its borders open to civilians fleeing the unrest in Burundi and granted them prima-facie refugee status but has warned that it can only accommodate about 50,000.