In a communiqué issued unanimously by the UN Security Council, the Council called for immediate cessation of violence against civilians and stressed the importance of preserving human rights.
The call comes from major powers around the world, a week after Russia and China blocked a similar statement on the Sudanese crisis.
More than 100 people were killed in a security operation against protesters in Khartoum on June 3, according to the Central Medical Committee, but officials say the toll is much lower.
On Sunday, a civil disobedience campaign was launched a week after the bloody attack on protesters in front of the General Command of the armed forces in Khartoum, which left dozens of dead, and the leaders of the protest accused the military council, especially the rapid support forces of its implementation.
The Security Council called on all parties "to continue to work together to find a compromise solution to the current crisis," expressing its support for African-led diplomatic efforts.
Diplomats say the draft, drawn up by Bahrain and Germany, was met with opposition from China and Russia, which refused to issue a condemnation, but in the end, the strong tone of the statement was approved.
The US Assistant Secretary of State for African Affairs Tibor Naji will arrive in Khartoum this week to discuss the crisis.
Talks between the military junta and protest leaders have been stalled over differences over whether the new transitional president would be civilian or military.
The Security Council will discuss the Sudanese crisis on Friday at a meeting focusing on the UN-African Union peacekeeping mission UNAMID in Darfur.