Pope Francis on Wednesday promised "friendship and respect" for all faiths at a meeting with representatives of major world religions in the Vatican in which he said he felt "close" to non-believers.

The Roman Catholic Church would "promote friendship and respect between men and women of different religions," the pope said, a day after his formal inauguration in St Peter's Square.

"We can do a lot for the good of people who are poor, who are weak, who suffer... and to promote reconciliation and peace," the pope told other Christian leaders and representatives of Buddhism, Islam and Judaism in an ornate Vatican hall.

Latin America's first pontiff said all religions should be united against "one of the most dangerous pitfalls of our time -- reducing human beings to what they produce and what they consume.

"I very much appreciate your presence and I see in it a sign of mutual respect and of cooperation for the common good of humanity," he said.

This was particularly important in a world of "divisions, confrontations and rivalries," he said.

Francis also told Jewish leaders he wanted to continue "a fraternal dialogue" that began with the reformist Second Vatican Council of the 1960s, which removed the notion of any Jewish blame for Jesus Christ's death in Catholic doctrine.

The 76-year-old pope also said he felt "close" to those people who "do not recognise themselves in any faith but are in a search for truth, for goodness and for beauty, which is God."

The reference echoed a "silent blessing" that Francis made on Saturday to non-believers at a meeting with journalists from around the world.

"You are all children of God," he said on Saturday.

Vatican expert Sandro Magister, who writes for the Italian weekly L'Espresso, said the references show "an attention to people without a religion" that was particularly significant as the Church struggles with rising secularism in many countries.

The Ecumenical Patriarch of Constantinople, Bartholomew I, the spiritual leader of the world's 250 million Orthodox Church, opened Wednesday's meeting.

Bartholomew was the first patriarch of Constantinople to attend a papal inauguration since 1054 when the eastern and western halves of Christendom split in the "Great Schism".

In his address, Bartholomew referred to Francis's experience as an archbishop in Argentina during that country's devastating economic crisis.

The world economic climate "demands humanitarian action for which you already have great experience," he said, referring to the "high, grave and difficult task" that Francis will face.

He said Christian unity was "our first and most important concern" and called on the pope to "correct worldly tendencies" in Christianity.

Francis assured Bartholomew -- whom he referred to as his "brother" -- of his "firm willingness to continue with the path of ecumenical dialogue".

Magister said these assurances were very much "in line with his predecessor" Benedict XVI, who was a keen promoter of inter-religious dialogue.

Francis on Wednesday also met with Brazilian President Dilma Rousseff, a former leftist guerrilla fighter and atheist, who leads the country with the highest number of Catholics in the world.

The Vatican said Rousseff had invited the pope to visit Rio de Janeiro for World Youth Day in July but did not say whether the pope had accepted.