He gave a sermon during an ecumenical service at Lund Cathedral commemorating the Reformation that split the Catholic Church in two and gave birth to the Lutheran denomination, which is the largest religion in Sweden.
There were alternating prayers during the service by the pope and heads of the Lutheran World Federation in which they asked for forgiveness for the deaths and pain their divisions had caused in the past.
Francis prayed that the Holy Spirit "help us to rejoice in the gifts that have come to the Church through the Reformation, prepare us to repent for the dividing walls that we, and our forebears, have built, and equip us for common witness and service in the world".
Francis was met by Prime Minister Stefan Löfven when his plane landed in Sweden, before he met members of Sweden's royal family, including King Carl XVI Gustav and Queen Silvia.
There were crowds of people gathered to greet his arrival in Lund, which marks the first papal visit to Sweden for 27 years.
He later attended a second ecumenical event at Malmö Arena in front of a large crowd.
Although the Reformation started in Germany when monk Martin Luther nailed his 95 Theses to the door of his Catholic church, Monday's events took place in Lund since the Lutheran World Federation was founded there in 1947.
In the run-up to the pope's visit, voices from both denominations questioned whether there is anything worth celebrating about the divide that has at times lead to violent clashes between Catholics and Protestants.