Travellers barricaded themselves at the camp at Crays Hill near Basildon, Essex, throughout Monday as bailiffs waited for the green light to remove cars and caravans.
However, a temporary reprieve was granted by a High Court judge to the consternation of Basildon Council, which was told it must clarify its intentions towards each plot by noon on Wednesday.
In a joint statement, the Anglican Bishop of Chelmsford, the Rt Rev Stephen Cottrell, and the Roman Catholic Bishop of Brentwood, the Rt Rev Thomas McMahon, said they were committed to negotiating a "peaceful settlement" to the Dale Farm dispute.
"We are both deeply distressed by what is occurring on the site and we are praying for a peaceful and equitable outcome for all parties concerned," they said.
The Rev Paul Trathen, an adviser to the Bishop of Chelmsford, was at the site to offer support to the travellers.
The gypsy community bought the land at Dale Farm 10 years ago and built their camp on the six-acre site without planning permission. They were reportedly offered an alternative site in Merseyside, but turned it down.
Attempts to move them off the land have been criticised by the Council for Racial Equality and the United Nations.
Speaking before yesterday's High Court intervention, Bishop Cottrell said the situation at Dale Farm was a "tragedy" that "illustrates a breakdown in planning and providing adequate site for travellers".
"Nobody is above the law but nobody should be placed outside the law. That is what is happening to the travellers," he said.
"This is a national problem that can only be resolved by the government.
"The government must address the planning and provision of traveller sites urgently."