Pope Francis has given the first Sunday Angelus prayer of his papacy to a crowd of more than 100,000 in St Peter's Square.

Breaking with tradition, Pope Francis delivered off-the-cuff remarks, about God's power to forgive, instead of reading from a written speech.

The crowd roared in delight.

Pope Francis began his first Sunday as pontiff by making an impromptu appearance to the public from a side gate of the Vatican.

He startled passersby and prompting cheers, then kept up his simple, spontaneous style by delivering a brief, off-the-cuff homily at the Vatican's tiny parish church.

Dressed only in white cassock, Pope Francis waved to the crowd in the street outside St Anna's Gate.

Before entering the church, which serves Vatican City State's hundreds of residents, he shook hands of the parishioners and kissed babies.

In keeping with his informal style, Pope Francis then went over to the chief of his security detail and appeared to indicate he wanted to greet two priests in the crowd, who approached and embraced him.

The impromptu appearance came more than two hours ahead of his first appointment of his papacy with the faithful from his studio window overlooking St Peter's Square.

After the Mass, the Pope stepped out jauntily from St Anna's Church and waved to a crowd of hundreds kept behind barriers across the street and then greeted the Vatican parishioners one by one.

One young man patted the Pope on the back in an indication of the informality that from the first moment of his papacy has been evident.

"Francesco, Francesco," children shouted his name in Italian from the street.

As he patted one little boy on the head, he asked "Are you a good boy?" and the child nodded. "Are you sure?" the Pope quipped.

In his homily, Francis spoke only five minutes, saying the core message is "that of mercy".

Meanwhile, Pope Francis has sent out his first tweet saying: "Dear friends, I thank you from my heart and I ask you to continue to pray for me. Pope Francis."