“Fear brought me here,” said Ely Ould Mohamed, who raises goats and fled Lerneb, a village between Goundam and the Mauritanian border. “There’s M.N.L.A. and Ansar Dine in my zone. Nothing is going right. Most people have already left. And the people are living miserably.” He was standing in the back of a pickup with his wife and five children, and had traveled six days by donkey cart to reach the border.

“People are living in fear, and they are leaving,” said Abuba Ag El Mostapha, a farmer of 65 who had come with five children from Duenza, south of Timbuktu. He spoke of numerous arrests in the town carried out by the Gandakoy, an armed faction that has allied itself with the Islamists.

In the document filed in The Hague, Malian officials reported “summary executions of soldiers, rape of women and young girls, massacres of civilians and the use of child soldiers and pillage.” Also documented were the destruction of hospitals, courts and schools as well as attacks on churches, tombs and mosques.

Fatou Bensouda, the court’s chief prosecutor, said she had instructed her staff to act quickly to establish if the court can have jurisdiction in the case, which made Mali the fourth African country to bring a case of its own volition to the court.

At the border, dozens of the very newest arrivals squatted patiently under a metal-roofed shelter, waiting to be registered in a few dusty adjoining outbuildings at the edge of the village, in an operation overseen by the United Nations. They then received a quick medical checkup, with the children’s tiny arms measured by a nurse for malnutrition.

One by one, the refugees trickled in to the registration building. “We don’t even know who to be afraid of anymore, the Salafists, the M.N.L.A., or the Mali army,” said Hama Ould Mohamed Bechir, standing in front of the desk. He had just fled the town of Léré, where M.N.L.A. officials recently claimed they were in control.

“There are a lot of armed people, coming and going all the time,” he said, including the men with long beards — the Islamists. “There’s some of everything,” said Mr. Bechir, who raises livestock.

Ely Ould Sidati had seen a lot of armed men at Léré — especially the bearded ones. He had heard gunshots, too. “I’m afraid, afraid of the war. We don’t want to be victims,” said Mr. Sidati, a shopkeeper.