Archbishop Desmond Tutu has waded into an ecclesiastical row over a New York church's refusal to allow protesters from Occupy Wall Street to camp on a vacant lot it owns.

The South African activist and retired church leader urged Trinity Church to heed the pleas of demonstrators to allow the camp and, failing that, at least to stop any violence or arrests at the site during a day of action this Saturday to mark its three month anniversary.

Tutu, the latest in a growing number of church leaders to align themselves with Occupy called the movement a "voice for the world."

A wave of evictions that has cleared encampments from cities and campuses across the United States has galvanised a clergy of different faiths to open their doors, and sometimes their homes, to protesters.

More than 1,400 church leaders, including the Rev Jesse Jackson have signed a pledge of support to OWS and on Wednesday, a coalition of prominent Afro-American pastors joined with the movement to launch a new series of actions that they consider part of the Rev Martin Luther King Jr's unfinished legacy.

But despite a cascade of support from these quarters, the protesters have failed to secure from their new allies the one thing they say they need to reignite the movement after having somewhat faded from the public radar – an outdoor space in which to gather, talk and plan.

The church has been steadfast it its refusal to allow a winter encampment. Photograph: Mark Lennihan/AP

Trinity is among the churches that have offered protesters some form of sanctuary, in their meeting rooms and offices and at their neighbourhood centre. However, despite weeks of negotiations, pressure from other church leaders and a hunger strike by four protesters, the church has been steadfast it its refusal to allow a winter encampment at its site at Duarte Square, at the corner of Canal Street and Sixth. Protesters have also criticised Trinity for not protecting them when they were arrested on the vacant lot on November 15.

Trinity Real Estate, the landowning arm of the church, has proposed a re-zoning plan to pave the way for up to 3,500 new housing units there, although it has yet to be approved by the community board. The plan also calls for a primary school.

In a letter to OWS, Tutu describes Trinity Church, on Wall Street, as an "esteemed and valued old friend" but said it caused him pain to hear of the impasse in negotiations between OWS and the church over the site.

"Sisters and Brothers, I greet you in the Name of Our Lord and in the bonds of common friendship and struggle from my homeland of South Africa. I know of your own challenges and of this appeal to Trinity Church for the shelter of a new home and I am with you! May God bless this appeal of yours and may the good people of that noble parish heed your plea, if not for ease of access, then at least for a stay on any violence or arrests."

He said: "I appeal to them to find a way to help you. I appeal to them to embrace the higher calling of Our Lord Jesus Christ – which they live so well in all other ways – but now to do so in this instance...can we not rearrange our affairs for justice sake?"

The matter is expected to come to a head on Saturday, during a day of action after a call to re-occupy former locations or find alternative camps.

Bishop George Packard, former chaplain for the armed services and decorated Vietnam veteran who has acted as the liaison in negotiations between the church and protesters, wrote on his blog this week that Duarte Square could be the new home for OWS "or not." He went on: "Trinity might mobilize platoons of police in riot gear and ring this sad little place with multiple barricades. No room at this Inn!"

Amin Husain, for OWS, has accused Trinity of putting "profit before God".

However, in a fresh posting on its website on December 9, the Right Rev John Cooper said that he believed that to allow a winter encampment would be "wrong unsafe, unhealthy and potentially injurious."

The rector stated:

"We want to be responsive, while also being responsible, to our residential and business neighbors, partners, visitors and tenants — our entire community. There are no facilities at the Canal St lot. Demanding access and vandalizing the property by a determined few OWS protesters won't alter the fact that there are no basic elements to sustain an encampment. The health, safety and security problems posed by an encampment here, compounded by winter weather, would dwarf those experienced at Zuccotti Park. "Calling this an issue of 'political sanctuary' is manipulative and blind to reality. Equating the desire to seize this property with uprisings against tyranny is misguided, at best. Hyperbolic distortion drives up petition signatures, but doesn't make it right. Those arrested [on November 15 at Duarte Square] were not seeking sanctuary; they were seeking to be arrested. Trinity will continue our responsible outreach and pastoral services for all."

Rev John Metz, of the Episcopalian Church of the Ascension, in Brooklyn, who is part of the Occupy In Faith NYC group, said collaboration between churches and the Occupy movement was gathering momentum. Supporters include Bhikkhu Bodhi, from the Buddhist Global Relief, and the Concord Baptist Church of Christ in Brooklyn, one of Amercia's largest protestant congregations.

"There's a natural relationship between the endeavours of the movement and of the church, both in terms of charity and looking at the source of societies ills," he said. "The dots are starting to be connected by the clergy and by lay people."

Metz, who has offered sanctuary to protesters in his own home as well as his church, said the Occupy movement was forcing church leaders to rethink their work.

"The Episcopalian diocese of Long Island, during its most recent convention, passed a resolution in support of Occupy Wall Street. What this means is that it becomes part of the Occupy Faith movement. Not only do you commit resources but you are re-occupying your own church by re-envisioning how it is we can live in ways that are committed to the Gospel mandate of social and economic justice. We are not asking people to 'like' this as on Facebook, but to work out the theology of occupation," he said.

He also called on the Archbishop of Canterbury to support the Occupy movement.

"It would be tremendously important if someone like the Archbishop of Canterbury were to step in with strong support of the Occupy movement. He understands the incarnated aspects of encampment. He understands that in terms of the Christmas story. We need his leadership here."

In a recent article in the Radio Times, a British magazine, Archbishop Rowan Williams posed the question "what would Jesus do" about the Occupy protesters at St Paul's. He suggested that Jesus would be there "sharing the risks, not just taking sides but steadily changing the entire atmosphere by the questions he asks of everybody involved, rich and poor, capitalist and protester and cleric" but he stopped short of coming out in support of the protesters.

The Rev Jackson also urged a stronger response from the Church of England to the Occupy movement on its doorstep. In front of St Paul's Cathedral in London on Wednesday, where he gave a speech hailing protesters as the direct descendants of the civil rights movement, Jackson said: "The church should be the headquarters for the Occupy movement. In a sense, the occupiers represent the conscience of the church."

While St Paul's reversed its initial decision to join action by the Corporation of London to evict protesters, relations between the camp and the church have been strained.

The Very Rev Jep Strait, from the Cathedral Church of St Paul in Boston, which has allowed demonstrators to hold general assemblies in the church since they were evicted, said: "This is very important to their central message about how society functions and who has access to power and resources and who doesn't which is also a part of the Gospel message."