VATICAN CITY 17 (Reuters) - The Roman Catholic Church, Church of England and al-Azhar, the Cairo-based seat of Sunni Muslim learning, came together on Monday for a rare display of interfaith action among them in calling for an end to modern slavery within 20 years.

Their joint statement setting up the "Global Freedom Network" they declared that "physical, economic and sexual exploitation of men, women and children" trapped 30 million people worldwide in slavery.

As well as establishing a world day of prayer for victims of slavery, the faiths agreed to "slavery-proof their supply chains and investments and to take remedial action if necessary" and press governments and companies to do the same.

Relations between the Vatican and the Church of England are cordial, even though they differ over women bishops and gay issues, while Rome's ties to al-Azhar are thawing after three years of frosty separation.

Bishop Marcelo Sanchez Sorondo, who signed the document for the Vatican, said Pope Francis had described human trafficking and modern-day slavery, raging from forced sex work to indentured agricultural labour, as a "crime against humanity".

He said the rare example of cooperation between the Catholic and Anglican communities and al-Azhar in Cairo could help build closer ties between the faiths.

"I think it's the first time we have worked together like this," he told journalists at the signing ceremony, adding that interfaith relations required careful study and treatment.

"But for other questions, human questions, the common values of humanity we can work together and this can be important for the theoretical path," he said.

CHALLENGE TO UNITE FOR POOR

Archbishop of Canterbury Justin Welby, head of the Church of England and the spiritual leader of the worldwide Anglican Communion, said in a statement that Anglicans and Catholic had been in close dialogue with each other since 1966.

"We are now being challenged in these days to find more profound ways of putting our ministry and mission where our faith is and being called into a deeper unity on the side of the poor and in the cause of the justice and righteousness of God," he said.

"We are struggling against evil in secret places and in deeply entrenched networks of malice and cruelty."

Al-Azhar froze relations with Rome in 2011 after then-Pope Benedict condemned attacks on Christians in Egypt, Iraq and Nigeria and said they showed the need for better protection of religious minorities in those countries.

Mahmoud Azab, who signed the agreement for al-Azhar's Grand Imam Sheikh Ahmed el-Tayeb, said the experience of the past three years of strained relations with the Vatican had shown that meeting simply to talk "was not sufficient".

After the election of Pope Francis a year ago, he said, "as soon as we saw positive signs, we resumed (contacts) right away. We were just looking for an agenda."

The initiative was associated with the Walk Free Foundation, a charity set up by Australian iron ore mining magnate Andrew Forrest to combat modern-day slavery.

Forrest said the campaign was not connected with efforts to improve conditions for low-paid workers around the world, which he said was a separate issue from slavery. But Azab said that minimally paid work could "prepare the ground" for slavery.

"I consider that being very badly paid, having a very, very low salary is part of slavery," he said. "Profiting from the needs of human beings, taking all their effort and energy without paying or paying very little, is part of slavery."

(Reporting By James Mackenzie; Editing by Tom Heneghan)