"We welcome the prohibition of inflammatory and hostile propaganda and insistence on the governments' obligation to protect their citizens," they said.
Late-April aerial bombardments, ground-force skirmishes and especially the increasingly hostile rhetoric of the leaders of Sudan and South Sudan had religious leaders worried about the possibility of all-out war.
The key problems are conflicting claims over oil revenues and the lack of a firm, internationally recognized border between Sudan and South Sudan, which became independent last July.
The bishops said they do not believe that "lasting peace will come unless all parties act in good faith. Trust must be built, and this involves honesty, however painful that may be."
In January, after a disagreement over the cost of transporting oil from landlocked South Sudan through Sudan, South Sudan shut down its oil production. Both nations have suffered economically from that decision.
The bishops acknowledged that the shutdown was popular with the people of South Sudan, but expressed concern "that stakeholders, both domestic and international, were not adequately consulted, and that the economic impact of the shutdown was not fully appreciated."
"We advise the government of South Sudan to continue to exercise restraint and to avoid doing anything that might be construed as military aggression," the bishops said, noting their concern at "the build-up of arms in both nations."
They called on the government of South Sudan "to ensure that basic services and good governance are delivered" despite economic problems.
There has been much building of roads and other infrastructure in Juba, South Sudan's capital, since independence, said John Ashworth, an adviser to the Sudan Ecumenical Forum, which includes the Catholic Church.
"Although development is slower in rural areas, there has been slow but steady progress," he said in a May 11 email to Catholic News Service.
But current problems due to the oil shutdown and the Sudanese government's "military adventurism are slowing things down now," Ashworth said.
Noting that the South Sudanese people and their government "are working hard to build a new nation," the bishops said they were ready to cooperate with them "to improve international awareness about key issues."
The bishops invited the international community "to walk with us on the painful journey of exploring the truth in competing claims and counterclaims, allegations and counter-allegations."
They committed themselves to "a renewed ecumenical effort to build peace," noting that they have much to offer Sudan's Council of Churches "as it restructures to meet the new reality of two nations and as it faces new challenges due to the current military and political tensions."