Kenya's President William Ruto said on Sunday that he was ready for "a conversation" with thousands of "peaceful" young protesters who held nationwide demonstrations this week to oppose proposed tax increases.

Organised on social media and led largely by Gen-Z Kenyans who have livestreamed the demonstrations, the protests have caught Ruto's government off-guard, as discontent mounts over his economic policies.

"I am very proud of our young people... they have stepped forward peaceful and I want to tell them we are going to engage them," Ruto said in his first public comments on the protests.

"We are going to have a conversation so that together we can build a greater nation," Ruto said during a church service in the Rift Valley town of Nyahururu.

His characterisation of the protests as "peaceful" came after rights campaigners reported two deaths following Thursday's demonstrations in Nairobi.

There was no immediate response to his remarks from the protesters, who have called for a national strike on June 25.

The demonstrations were mostly peaceful, but officers fired tear gas and water cannon throughout the day to disperse protesters near parliament.

A Kenya Human Rights Commission official said on Saturday that 21-year-old Evans Kiratu was "hit by a tear gas canister" during the protests and died in hospital.

On Friday, a police watchdog said it was investigating allegations that a 29-year-old man was shot by officers in Nairobi after the demonstrations.

The Independent Policing Oversight Authority (IPOA) said it had "documented the death... allegedly as a result of police shooting" on Thursday.

Several organisations, including Amnesty International Kenya, said that at least 200 people were injured in the protests in Nairobi, as thousands of people took to the streets across the country.

Following smaller-scale demonstrations in Nairobi on Tuesday, the cash-strapped government agreed to roll back several tax hikes laid out in a new bill.

But Ruto's administration still intends to increase some taxes, defending the levies as necessary for filling its coffers and cutting reliance on external borrowing.

Kenya has a vast debt mountain, and servicing costs have ballooned due to a fall in the value of the local currency over the last two years, leaving Ruto with few options.

The tax hikes will pile further pressure on Kenyans, with many already struggling as the cost of living surges and well-paid jobs remain out of reach for young people.

Ruto said on Sunday that the annual budget included measures to tackle youth unemployment and improve access to higher education.

"What I want to assure (the protesters)... is that we are concerned about their issues," he said.

"We are going to make sure that every child has access to higher education."

After the government agreed to scrap levies on bread purchases, car ownership as well as financial and mobile services, the treasury warned of a 200-billion-shilling (US$1.5-billion) shortfall.

The government has now targeted an increase in fuel prices and export taxes to fill the void left by the changes, a move critics say will make life more expensive in a country already saddled with high inflation.

Kenya is one of the most dynamic economies in East Africa but a third of its 51.5 million people live in poverty. (AFP)