A global and regional church body called for "maximum restraint" by Sudan and South Sudan forces amid an armed dispute that has escalated into violence in the past two weeks along a border established last year.

The heads of the World Council of Churches and All Africa Conference of Churches, in an open letter dated Tuesday, expressed "grave concern" and called for "maximum restraint" on both sides to avoid further deterioration of the situation.

"We call for mutual respect of the territorial integrity of each other's state," said WCC General Secretary Dr. Olav Frykse Tveit and AACC General Secretary Dr Andre Karamaga in a statement.

South Sudan's army occupied the oil town of Heglig earlier in April, a move accompanied by the deadliest fighting among the sides since South Sudan officially seceded from the north last July. Heglig produces about half of Sudan's oil.

The church body leaders say they "advocate for a just and peaceful resolution of the conflict starting with immediate ceasefire."

The groups also called for talks and the use of the use of the previously agreed to Comprehensive Peace Agreement to serve as a guide for their interaction.

"We implore the parties to use the CPA as the framework and model for resolving the border issue and all other outstanding issues," they said.

They called for civil groups to double their diplomatic efforts, calling on the Government of Kenya, the Intergovernmental Authority on Development, African Union and the international community to do so.

"The WCC and the AACC wish to assure the Sudanese churches and people of our prayerful support and solidarity in seeking a peaceful solution to the prevailing conflict. We are prepared at any and all times to be at the disposal of the Sudan Council of Churches and its member churches and work together to save lives and promote peace, healing and reconciliation in South Sudan and Sudan."