"The wrongdoings of the past are a cause of the greatest sorrow and the deepest regret," Charles said during a speech later in the day.
But he stopped short of making a full apology for the abuses committed by British colonial forces, especially in the 1950s, as demanded by survivors of that period.
"There were abhorrent and unjustifiable acts of violence committed against Kenyans as they waged... a painful struggle for independence and sovereignty – and for that, there can be no excuse," he said.
During the visit, Charles is expected to acknowledge the "painful aspects" of the British colonial rule in East Africa, which lasted almost seven decades.
This year, Kenya celebrates the 60th anniversary of its independence.
Royals to 'deepen understanding' of colonial period
Charles was received by Kenyan President William Ruto in the capital, Nairobi.
Buckingham Palace said the visit is a reflection of the UK and Kenya's close cooperation on economic development, climate change and security.
Charles and his wife Camilla will tour a new national history museum and visit the site where Kenya's independence was declared in 1963.
He is also scheduled to visit Nairobi National Park and meet with environmental activist Wanjira Mathai.
"His Majesty will take time during the visit to deepen his understanding of the wrongs suffered in this period by the people of Kenya," the palace said.
The British High Commission said Charles would also "meet veterans and give his blessing to efforts by the Commonwealth War Graves Commission to ensure Kenyans and Africans who supported British efforts in the World Wars are properly commemorated."
The UK government has previously expressed regret over abuses committed during the colonial period, most notably during the 1952-1960 Mau Mau revolt in central Kenya. The Kenya Human Rights Commission (KHRC) estimated that 90,000 people were killed or maimed and 160,000 detained by colonial authorities during the uprising.
In 2013, London agreed to an out-of-court settlement of almost 20 million pounds over the military operations that put down the Mau Mau rebellion.
At last year's Commonwealth summit, Charles acknowledged the role of slavery in the British Empire's history.
rm, sdi/rc (Reuters, AP)