Francis is greeted by screams as he delivers message at St Peter's, saying thoughts at Christmas turn to the most vulnerable

Pope Francis has addressed his first Christmas message to every man or woman "who hopes for a better world, who cares for others while humbly seeking to do his or her duty".

He appeared at the vast balcony at the front of St Peter's basilica to be greeted by screams fit for a pop star. Below him in St Peter's Square was a crowd brimming with enthusiasm for the new pontiff and his humble, ascetic and socially aware form of Catholicism.

That view of his faith was at the heart of his address. "Looking at the child in the manger, our thoughts turn to those children who are the most vulnerable, victims of wars, but we think too of the elderly, of battered women, of the sick," he said.

"He exemplifies what a pope should be," said Marian Merrett from Belleville, Ontario. "He's like Jesus. Jesus too fed the poor and cared for the sick. He exemplifies what Jesus stood for. He lives like Jesus."

In his sermon at the Christmas Eve mass, Francis had returned to his favourite theme, declaring that the shepherds who according to the gospels were the first to see Jesus after his birth "were the first because they were among the last, the outcast".

"This is the pope we've been waiting for for a long time," said Anna Maria Pistorio as she waited by the barriers erected in St Peter's with her arm around her son, Luca, who has Down's syndrome. Pistorio, a postal worker, and her husband had travelled down from Vimodrone near Milan to be with their other son for Christmas and had taken the opportunity to come and listen to the pope.

"The churches have been emptying out," said her husband, Palmiro Gattella. "But this pope has given vigour to the church, and hope to many. The church has come down from among the powerful to be with the people."

The loudest cheering – and most of the screaming – came from a group of schoolgirls at the very front of the crowd who had arrived from a school in Rhode Island run by the Legionaries of Christ – a group that has much to fear from this papacy. Among the topics awaiting the pope's attention in the new year is a meeting in Rome at which the organisation – wracked by accusations of sexual abuse – is expected to be split up.

Francis was unable to shed totally the trappings of papal authority. The balcony of the mighty basilica was draped with rich velvet for the occasion. The basilica and the square exude pomp and majesty.

But the hallmarks of his style – the direct, almost conversational manner of speech and concern for those on the margins of society – were prominent in his address to the crowd, estimated by the Vatican as 70,000.

As is customary, he appealed for peace in a long list of countries topped by Syria. He also mentioned the Central African Republic "often forgotten and overlooked", South Sudan, Nigeria "rent by constant attacks which do not spare the innocent and defenceless", and appealed to God for a favourable outcome to peace talks between Israelis and Palestinians.

But he also had a word for migrants and expressed the wish that "tragedies like those we have witnessed this year, with so many deaths at Lampedusa, never occur again". The pope prayed that the spirit of Bethlehem would "touch the hearts of all those engaged in human trafficking, that they may realise the gravity of this crime against humanity."