The Pope urged Christians to "embrace hospitality" and reject the "logic of selfishness".
The Paraguay visit was the culmination of the Pope's eight-day tour of some of South America's poorest countries.
During his previous stops in Bolivia and Ecuador, he spoke out against social injustices in the region.
He also apologised for the role of the Roman Catholic Church in the brutal colonisation of most of Latin America by the Spanish.
"Welcome the hungry, the thirsty, the stranger, the naked, the sick, the prisoner, the leper and the disabled," Pope Francis spoke at the Mass in Asuncion.
"Welcome those who don't think like us, those who don't have faith or have lost their faith."
Earlier the Pope visited the Banado Norte shantytown in Asuncion, home to some 100,000 people.
He urged residents to stand up for each other.
"No matter how many Masses on Sundays, if you don't have a heart in solidarity, if you don't know what is happening in our town, your faith is very weak, or it's sick or it's dead."
Pope Francis, who was born in Argentina, is the first leader of the Roman Catholic Church to come from Latin America.
Thousands of people travelled from neighbouring Argentina for the Pope's last Mass in the tour, including President Cristina Fernandez de Kirchner.
Hundreds of thousands of people have attended the final Mass celebrated by Pope Francis during his visit to Paraguay.