A Bangladesh Air Force training aircraft crashed onto a school campus in Dhaka, the capital, on Monday afternoon, killing at least 20 people and injuring 171 others, military officials said.

The Bangladeshi military said in a statement that a mechanical error had caused the crash, which occurred at Milestone School and College in an area called Uttara, north of the city’s international airport and a military air base. More details will be released after an investigation, the statement said.

The plane was an F-7 BGI, a Chinese fighter jet that is based on a Russian MiG design. Bangladesh bought its F-7s in 2013.

As students joined in the rescue effort and residents lined up to donate blood, police officers, military personnel, fire officials and emergency workers struggled to contain large crowds that had gathered around the campus.

Helicopters and dozens of ambulances transported injured people to a hospital that specializes in treating burns, officials said.

The fighter jet, which took off shortly after 1 p.m. from an air base near the international airport, crashed into the second floor of a school building where third and fourth graders were, Brig. Gen. Muhammad Jahed Kamal, the director of Bangladesh’s national fire department, told reporters. The school has students from elementary to high school grades.

An initial report by the armed forces said that the pilot, who the military said died in the crash, had tried to maneuver the plane to a less populated area.

One high school student, Emon Islam, said that he had been near the campus when the plane crashed. “I saw the windows of the aircraft shattered, and it was burning up in flames, with black smoke rising into the sky,” Mr. Islam said.

In the early hours after the crash, the mother of another student, Ambia Akter, said that her son, Wasif Kader Bhuiyan, an 18-year-old in the 12th grade, was trapped inside the building and that she had not been able to reach him.

“I was trying to enter the campus building, but it was not possible due to a heavy crowd,” she said in an interview. “I don’t know what happened to him.”

By 8:30 p.m., the fire services reported that rescue operations were finished. An hour later, ambulances were still ferrying patients to the National Institute of Burn and Plastic Surgery, one of the biggest specialized centers in the world, from other hospitals.

Families of the injured students and other victims massed outside the institute’s gates, waiting. Hundreds of people lined up to donate blood, so many that hospital workers had to ask them to leave.

Muhammad Yunus, the leader of Bangladesh’s interim government, said that the government was investigating the cause of the crash and that he was praying for the speedy recovery of those injured. “The loss suffered by the Air Force, the students, parents, teachers and staff of Milestone School and College, as well as others affected by this accident, is irreparable,” he said in a statement.

Sayedur Rahman, a special assistant to Mr. Yunus, told reporters outside the burn institute that most of the wounded were children, that 25 were in critical condition and that nine were in the center’s intensive care unit. Among the 17 dead the authorities were able to examine, seven bodies could not be identified immediately because of the severity of their burns.

Shawkat Ali was the uncle of one of the victims taken to the burn institute. “We heard that my nephew is no more, that he died,” he said. “We haven’t seen his body yet.”

His nephew, he said, was an eighth grader named Tanvir Ahmed.

“He was a very good student,” Mr. Ali said. “He was on the second floor of the building. We are now waiting for the body.”

Ms. Akter, the mother of the missing 12th grader, was more fortunate. After seven hours of worry, her son, Wasif, she said in a later interview, turned up, alive and healthy.

By Monday evening, officials had not released the names of any of the dead beyond that of the pilot. The government declared Tuesday a national day of mourning, with flags to fly at half-staff at public buildings and other institutions and special prayers to be held at places of worship.

Alex Travelli contributed reporting from New Delhi, and Maruf Hasan from Dhaka.