The pontiff was speaking on the first day of his trip to the country.
He said the country had to pursue the truth behind injustices committed during the conflict but did not specifically refer to Sri Lanka's refusal to co-operate with a United Nations investigation.
The UN wants to look into alleged war crimes after a 2011 report said up to 40,000 Tamil civilians may have been killed and that both sides committed serious human rights violations.
The Holy Father gave the speech at Colombo airport after being welcomed by new president Maithripala Sirisena.
It's the first trip of a pope to the nation since the war ended in 2009 and Francis is hoping to bring reconciliation.
He said finding a lasting peace "can only be done by overcoming evil with good, and by cultivating those virtues which foster reconciliation, solidarity and peace".
He added: "The process of healing also needs to include the pursuit of truth, not for the sake of opening old wounds, but rather as a necessary means of promoting justice, healing and unity."
Meanwhile the new President Maithripala Sirisena is being urged to uphold his election pledge to promote freedom of religion or belief.
The National Christian Evangelical Alliance of Sri Lanka says that incidents of religious intolerance and violent attacks increased from 52 in 2012 to 103 in 2013.
Sri Lanka has come under attack for its human rights record under former President Mahinda Rajapaksa.
Christian Solidarity Worldwide's Chief Executive Mervyn Thomas said: "In his manifesto, President Sirisena acknowledged the need to protect religious minorities from the threat of violence from extremist groups and we welcome his commitment to ensuring religious harmony in Sri Lanka.
"We encourage the new Government of Sri Lanka to prioritise measures to address the violence and discrimination suffered by its religious minorities, especially Christians and Muslims, and to guarantee freedom of religion or belief for its citizens."