Burundi's constitutional court cleared President Pierre Nkurunziza to run for a controversial third term Tuesday, as the government offered to release protesters if days of deadly demonstrations stopped.

The court ruled that the president's bid to stand for another term "by direct universal suffrage for five years, is not contrary to the constitution of Burundi," the judgement signed by six out of seven judges read.

U.S. Secretary of State John Kerry warned Monday that the bid by Burundi's president to run for a third term in power goes against the constitution, calling for calm after days of protests.

"We are deeply concerned about President Pierre Nkurunziza's decision, which flies directly in the face of the constitution of this country," Kerry told reporters in the Kenyan capital Nairobi.

Police in Burundi shot dead at least four demonstrators and wounded dozens of others Monday, in running battles with protesters angry at a bid by President Pierre Nkurunziza to extend his rule.

The deaths, which leading human rights activist Pierre-Claver Mbonimpa confirmed, brought the death toll in more than a week of protests to at least 13, including two soldiers and a policeman.

Journalists in Burundi held a sombre gathering Sunday to mark World Press Freedom Day, after a week of political violence that has also seen radio stations shut down.

"It's a sad day for the Burundian press because radio stations are closed, journalists are jailed," said Antoine Kabuhare, head of an independent media rights group.

Three people were killed Friday in grenade attacks on police in Burundi where nearly 600 people have been arrested during protests and clashes sparked by the president's bid to stay in power.

The director general of police, General Andre Ndayambaje told Agence France Presse two officers were killed and one was wounded in the attack in Kamenge district of the capital Bujumbura, while a local resident said a civilian also lost his life and two others were wounded.

At least seven people have died and 66 others wounded in nearly a week of clashes between police and protesters in the central African nation of Burundi, officials said Friday.

Giving an overall toll of those injured in the violence, Burundian Red Cross spokesman Alexis Manirakiza said 29 people were hurt in Thursday's clashes, bringing to 66 the number of wounded since the violence began on Sunday.

A Burundi soldier was shot dead by an intelligence officer while at least nine protesters were hurt in renewed clashes in the capital Thursday over a bid by the president to stand for a third term.

The soldier died and a civilian was hurt when the intelligence officer opened fire near a barricade erected by protesters in Bujumbura, said a senior police officer speaking on condition of anonymity.

U.N. rights experts on Thursday warned that Burundi could lapse into fresh conflict following the president's move to extend his mandate in upcoming polls which has provoked deadly clashes.

At least six people have died in the central African nation since the ruling CNDD-FDD party at the weekend designated President Pierre Nkurunziza as its candidate in the next presidential election due at the end of June.

At least nine protestors were hurt in Burundi's capital Thursday in renewed clashes over a bid by the country's president to stand for a third term, the Red Cross said.

The national organization confirmed that the overall death toll from days of violent protests now stands at six dead.

Protest-hit Burundi on Wednesday took the controversial question of President Pierre Nkurunziza's third term bid to the constitutional court but opposition supporters dismissed the move and said demonstrations would go on.

At least five people have died since unrest broke out at the weekend, when the ruling CNDD-FDD party designated Nkurunziza its candidate for the presidential election to be held in the central African nation on June 26.