DAMASCUS, Syria — Facing extraordinary challenges, millions of Syrian children in government-controlled areas returned to school this week despite the civil war that has left almost 4,000 schools — one in five — damaged, destroyed or sheltering displaced families.

In Damascus, the Syrian capital, a frequent target of mortar shells fired by rebels entrenched in the suburbs, the government insisted on starting the academic year on time, despite the constant threat.

At the Suleiman Hassan Shuaib school in the upscale Mazzeh neighborhood of Damascus, children and parents greeted the start of school with a mix of anticipation and concern.

Principal Ali Ali said many of the school’s 500 students are newcomers who transferred from schools in war-shattered towns across the country. The school now uses an underground depot as a shelter in case of emergency, and employs a psychologist to deal with students suffering fear and trauma.

“It’s normal that the habits of some pupils have changed, but in general, a large number of them look courageous and show indifference to what is happening,” said Raneem Diab, the psychologist.

She added that the worst hit were the new arrivals from schools in the, where fighting between government forces and rebels has raged for months.

“Regretfully, what is happening affects children, but we are trying to raise their morale and bring them up properly despite these difficult circumstances,” she said.

Children’s activities have been restricted because of the war, so parents said the start of school was a chance to meet friends and have fun after a summer spent confined to home.

A recent report by the charity Save the Children estimated that thousands of children have not attended school in the past two years. It warned that the war is reversing one of Syria’s main prewar achievements — in 2010, nearly all children had completed primary school.