During a speech to young people in the Kenyan capital, Nairobi, he got the audience to hold hands to symbolise that they stood together as one nation.
Kenya was shaken by inter-ethnic violence after elections in 2007 in which 1,200 people died.
The pontiff also made an impassioned plea against corruption, saying: “Corrupt people don’t live in peace.”
The BBC’s Ruth Nesoba at the Kasarani stadium, where the Pope spoke about issues affecting young people, says the crowd cheered wildly when he condemned corruption and urged them not to accept bribes.
“Each time… we put it in our pockets, we destroy our hearts – we destroy our personalities and we destroy our country. Please don’t develop that taste for that sugar that is corruption.”
Overcoming tribalism would be a daily endeavour that would require Kenyans to listen one another to avoid division, he said.
“I want to invite you all – that we hold each other’s hands – let’s hold hands together, let’s stand up as a sign against bad tribalism – we are all a nation.”
Pope Francis also addressed radicalisation in a country which has suffered several serious attacks by Islamists from the Somalia-based al-Shabab group.
“If a young woman or man has no work, can not study, what can he or she do? The first thing we have to do to stop a young person to be recruited is education and work.”
‘End land grabbing’
Earlier, the pontiff was cheered as he arrived at his first stop of the day in Kangemi, which is home to tens of thousands of people living in cramped rooms, usually without running water and basic sanitation.
He criticised private developers for grabbing land from poor people, referring to an incident earlier this year when police fired tear gas at children protesting against developers trying to take over their playground.
He was also critical of wealthy minorities indifferent to the plight of the poor and called for improved living conditions and infrastructure in urban areas – including drinking water and schools.
It was a duty for all to ensure that the poor in urban areas had the “three Ls” – access to land, lodging and labour, he said.
The Pope will go to Uganda later on Friday, before travelling to the Central African Republic (CAR) on Sunday.