He arrived in Kenya on Wednesday, at the start of a three-nation tour of Africa.
President Uhuru Kenyatta and ululating crowds welcomed him at the airport in the capital, Nairobi.
The Pope said conflict and terrorism fed “on fear, mistrust, and the despair born of poverty and frustration”.
The pontiff played down security fears about his trip, joking that he was “more worried about the mosquitoes.”
A leading Muslim cleric in Kenya welcomed the visit, saying it gave hope to the “downtrodden in the slums”.
An atheist group said it would challenge in court a government decision to declare Thursday a holiday in honour of the pontiff.
Pope Francis’s five-day visit will also see him go to Uganda and Central African Republic, which has been hit by Christian-Muslim conflict.
Kenya’s government has said that up to 10,000 police officers may be deployed during the visit.
Militant Islamists have carried out a series of attacks in Kenya – including the 2013 siege at Nairobi’s Westgate shopping centre, which left at least 67 dead, and the killing of about 150 people during an assault on the Garissa National University College in April this year.
Welcomed in Latin
“All men and women of goodwill are called to work for reconciliation and peace, forgiveness and healing,” Pope Francis said at a function hosted by President Kenyatta in State House.
Pope Francis also warned of the “grave environmental crisis” facing the world, and said leaders needed to promote “responsible models of economic development”.
He made a veiled reference to corruption by calling on leaders to work with integrity and transparency, says the BBC’s Joseph Odhiambo in Nairobi.
President Kenyatta called on the Pope to pray that Kenya succeeds in its fight against corruption.
On Wednesday, he sacked six ministers following allegations of corruption in the government. The six have denied the allegations.
Religion in Sub-Saharan Africa:
- Christian population is 517 million (63% of total)
- Protestants make up more than half the number
- Catholics make up about a third
- Muslim population is 248 million (about 30% of total)
- 1.1 billion Christians expected by 2050
- 670 million Muslims expected by 2050
Source: US-based Pew Research Center 2011 survey
About 30% of Kenyans – including President Kenyatta – are baptised Catholics, and there is huge excitement around the visit, our correspondent says.
Crowds lined the streets of Nairobi to catch a glimpse of the pope as he was driven in a grey Honda saloon to Mr Kenyatta’s office for his official engagement.
One of Kenya’s main newspapers, The Standard, welcomed him with headlinesin Latin, Grata Franciscus Pontifex, and the regional Swahili language, Karibu Papa Francis.
The Pope is expected to tackle corruption, poverty and religious conflict during his five-day visit.
Abdalla Kwamana, the vice-chairman of the Supreme Council of Kenya Muslims, said he would attend an inter-faith meeting the pontiff is hosting on Thursday.
He described the visit as highly significant, and welcomed the Pope’s decision to include a shantytown in his itinerary.
“It is often said that Kenya is owned by the rich and powerful. The people in the slums are never recognised,” Mr Kwamana told the BBC’s Newsday programme.
“When he goes to see them and console them, they’ll feel they are people of substance,” he added.
Pope Francis is due to hold a mass on Thursday at the University of Nairobi sports ground, where a crowd of more than one million is expected, Kenya’s private Daily Nation newspaper reports.
The tiny Atheists in Kenya group said the decision to declare Thursday a public holiday and a day of prayer was unconstitutional.
“The constitution clearly states that there shall be no state religion. We cannot have the government acting religiously,” its leader Harrison Mumia said, Nation FM radio station reports.
One in six of the world’s Catholics are in Africa.