Steve Clifford, general director of the Evangelical Alliance, said that the vote and the "bruising" campaign in the lead up to it had exposed deep disagreement across the UK and the "fragility" of British democracy.
"The UK is not united," he said. "We have entered a time of enormous uncertainty, not only as we renegotiate our relationship with our European neighbours, but also as the governing Conservative party begin the process of selecting our next prime minister."
He continued by saying that the aftermath of the referendum called for a time of prayer, as he issued a challenge to the church to build unity and model reconciliation.
"We have taken a significant decision and in the coming years many more will need to be taken," he said.
"Although we have chosen to leave the EU we remain part of Europe and need to remember our responsibilities to support and care for our neighbours. In the months and years to come we have to model with generosity what a difference love and friendship can make.
"Our energies must now be directed towards building bridges within and between communities across the UK.
"We have confidence in God who holds the nations in His hands, who is the creator of all things. We have confidence that though the pundits and pollsters may be flummoxed, God is not fazed."
"In the light of the result we believe churches should be places where disagreement does not lead to division," the EAUK said.
Its call was reiterated by the World Evangelical Alliance. Its Secretary General, Bishop Efraim Tendero, asked Christians to join in prayer for the people of the UK and the EU after the vote, and particularly the governments now tasked with difficult negotiations and the exit process.
"Let us follow the words of the Apostle Paul that he wrote in his letter to Timothy: 'I urge, then, first of all, that petitions, prayers, intercession and thanksgiving be made for all people - for kings and all those in authority, that we may live peaceful and quiet lives in all godliness and holiness.'"
