Kenya's President Uhuru Kenyatta has apologised for violence by the police following the enforcement of a nationwide curfew last week.

The police have been accused of using heavy-handed tactics to enforce the dusk-to-dawn curfew since its introduction on Friday to mitigate the spread of the coronavirus pandemic, with tear gas, baton charges and the alleged firing of live rounds.

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"I want to apologise to all Kenyans for ... some excesses that were conducted," President Kenyatta said on Wednesday in Nairobi.

"But I want to assure you that if we work together, if we all understand that this problem needs all of us, and if we pull in the same direction, we will overcome."

The police also ordered an investigation into the shooting of a 13-year-old boy who died in the capital Nairobi on Monday after being shot while standing on his balcony as police forced people into their homes.

The victim's father, Hussein Moyo, told AFP news agency that the bullet had "ripped through his intestines".

"This operation was planned in the wrong way. The police arrive yelling and when people see that they run scared. They beat and rob people, they also throw tear gas into our houses," Moyo said.

"During the day we are fighting coronavirus, and yet we have to deal with bullets during the night."

Sporadic clashes have also been reported in the western city of Kisumu and the port town of Mombasa where officers chased and beat commuters and fired tear gas last week.

The curfew is among measures that Kenya has taken to slow the spread of coronavirus. It has also closed borders and schools, and encouraged people to stay at home and avoid gatherings.

A lockdown has yet to be imposed, but Kenyatta said tighter restrictions had not been ruled out.

"We as a government are preparing for the worst, but together with the 47 million Kenyans, we are hoping and praying that we do not need to take further measures," he said.

Kenya has so far recorded 81 cases of coronavirus and one death.