The Christian charity and other organisations want a special session of the UN Human Rights Council on Sudan, after the military's deadly crackdown last week on protesters.
The African country has been suspended from the African Union as a result.
On Sunday, streets were empty across Sudan's capital on the first day of a general strike urged by protest leaders demanding the resignation of the ruling military council.
The Sudanese Professionals Association (SPA) called on people to stay at home in an act of protest.
The SPA spearheaded months of mass protests that led to the military overthrow of President Omar al-Bashir in April, and called on people to remain in the streets until a full handover of power to civilians.
CSWs Chief Executive Mervyn Thomas said: "We extend our deepest condolences to the families of those who have lost loved ones, and pray that the injured would soon recover.
"It has been a particularly difficult week for the Sudanese people, as the violence was launched just before Eid, the celebration of the end the Ramadan fast.
"We condemn these brutal attacks on innocent civilians in the strongest terms and welcome the African Union's decision to suspend Sudan from the regional body and stand in solidarity with the Sudanese people.
"There is an urgent need to restore civilian rule and hold those responsible for the lethal attacks on unarmed protestors to account."
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