Explosions killed at least five people and injured 50 in Burundi's largest city Bujumbura on Monday night, the prime minister and a health worker said after the latest in a string of attacks in the east African country.

The Interior Ministry said on Twitter that "unidentified terrorists" were responsible. There was no immediate claim of responsibility for the grenade attacks.

Two grenade explosions hit a bus parking lot in the city centre, according to seven eyewitnesses, while a third blast hit Jabe market in the Bwiza neighbourhood, according to another witness.

Five people were killed and about 50 wounded, a health worker helping to care for the injured told Reuters on Tuesday. The witnesses and the health worker requested anonymity.

A man in a bus hit by a grenade explosion said it killed at least three people including a woman. The blast injured his leg, he told Reuters while awaiting treatment.

"I saw people running in all directions, some crawling to find cover," said a witness to the second explosion at the bus parking lot.

During a visit to the wounded in hospital, Prime Minister Alain-Guillaume Bunyoni told reporters the attacks had killed two and promised government help for those wounded.

On Sunday, a grenade attack in the administrative capital Gitega killed two, according to local media. It was not clear who was responsible.

An airport worker confirmed there had been an attack on the Bujumbura airport on Saturday. He declined to say what weapons were used and said the building had not been damaged.

Congo-based rebel group Red Tabara claimed responsibility for the airport attack in a statement on Twitter. It said it fired mortars as the president prepared to travel to the United Nations General Assembly in New York.

Red Tabara was formed in 2011 with the aim of overthrowing the government, which it says does not respect the rule of law.

Burundians accused of having ties to the Congo-based rebels have been tortured and likely disappeared, Human Rights Watch said in a report on Friday.

Unidentified bodies have been found in the river separating Burundi and Congo in recent months, it said.

Burundi, a nation of about 11.5 million people, has suffered decades of war and ethnic and political bloodletting. The United Nations says the youth wing of the ruling party and the security services are complicit in the torture, gang-rape and murder of political opponents, charges the government denies.

(This story corrects number of dead attributed to prime minister to two instead of four, paragraph 7.)

Reporting by Nairobi Newsroom; Editing by Grant McCool