Francis said he was making the trip to show solidarity with Iraq's devastated Christian community of around 300,000, just one fifth of the number before the US invasion in 2003 and the brutal Islamist militant violence that followed.
Pope John Paul II came close to visiting, but had to cancel a planned trip in 2000 after talks with the government of then-leader Saddam Hussein broke down.
The 84-year-old Francis, limping from what appeared to be a fresh flare-up of his painful sciatica, made an impassioned call for Iraqis to finally give peacemakers a chance during a gathering of Iraqi officials and diplomats at the presidential palace.
He later paid tribute to people killed in attacks motivated by religion, visiting a Baghdad church where Islamist gunmen killed about 50 worshippers in 2010.
Iraq's security has improved since the defeat of Islamic State in 2017, but the country continues to be a theatre for global and regional score-settling, especially a bitter US-Iran rivalry that has played out on Iraqi soil.
The US invasion of 2003, after years of international sanctions and a devastating war with Iran instigated by former leader Saddam Hussein in the 1980s, plunged Iraq into sectarian conflict and chronic mismanagement that has plagued it since.
Following his meeting with Sistani, Francis is due to visit the ruins of ancient Ur in southern Iraq, revered as the birthplace of Abraham, father of Judaism, Christianity and Islam.
After flying back to Baghdad, he is expected to deliver mass at the Chaldean Cathedral of Saint Joseph.