The public ceremony for Father Jacques Hamel was led by the city’s archbishop.
French interior minister Bernard Cazeneuve and senior Roman Catholic clerics are attending the service.
Father Hamel had his throat cut when two men stormed his church during Mass.
More than 1,500 members of the congregation heard tributes from the a number of the priest’s family.
The priest’s sister Roselyne told the congregation that her brother, who was 85, had been a man of “mercy and love”.
She said he had turned down an officer position when doing his military service in Algeria, as the role would have required him to give the order for his men to kill other men.
“His refusal was categorical,” she said. “He chose to serve God so that he can cultivate love and sharing and tolerance among people of all faiths and denominations, believers and non-believers, throughout his life.”
She said Father Hamel’s message to everyone would be: “Let us learn to live together. Let us be the workers and artisans of peace, each one in his own way.”
“I love you, uncle,” said his niece Jessica Deleporte. She struggled to finish her words. “I will miss you.”
In the homily, Rouen Archbishop Dominique Lebrun said: “As brutal and unfair and horrible as Jacques’ death was, we have to look deep into our hearts to find the light.”
He called for forgiveness, quoting the New Testament command to love your neighbours.
Local Nicole Popelin, who watched the funeral, said: “No-one deserves to die like he did. We knew the Father very well. It hurts us so badly.”
And Hassan Houays, a Muslim maths teacher from Saint-Etienne, said: “We are here so that we can get along together. It is our duty.”
Father Hamel’s attackers – Abdel Malik Petitjean and Adel Kermiche – had both pledged allegiance to Islamic State. The pair, both aged 19, were shot dead by police after taking hostages.
A cousin of Petitjean has been arrested on suspicion of knowing he was planning the attack. Another man has been put under formal investigation for allegedly attempting to travel to Syria with Petitjean.
The attack on Father Hamel at a place of worship stunned France. It came shortly after the Bastille Day attack in Nice which left 84 people dead.
As part of its fight against radicalisation, the French government has announced the closure of 20 mosques.
It is also planning a new foundation to provide alternative funding for Islamic places of worship, amid concerns about the influence of Saudi Arabia’s ultra-conservative Wahhabi version of Islam.