A roof collapse at a tutoring centre under construction in Pakistan's eastern city of Lahore on Tuesday killed at least 14 schoolchildren, police and rescue officials said.

Eight other children were injured and were being treated in hospital, senior police officer Faisal Kamran said. He added that the owner of the tutoring centre and another person had been arrested.

Kamran said rescuers were searching through the rubble following reports that more children could be trapped beneath the debris. He said the tutoring centre was operating in an ageing building and that the roof of an unfinished second floor had apparently collapsed due to poor construction.

Building collapses are common in Pakistan, where construction standards are often poorly enforced. Many structures are built using substandard materials, while safety regulations are frequently ignored to reduce costs.

Witnesses said ambulances and rescue workers rushed to the scene after the roof collapsed. Local residents also joined the rescue effort, using shovels and their bare hands to clear the rubble in an attempt to reach children trapped underneath.

Hours later, as the bodies of the victims were handed over to their families, scenes of grief unfolded outside hospitals and in the neighbourhood on the outskirts of Lahore where the private tutoring centre was housed in a residential building. Parents wept over the loss of their children, while mothers and other female relatives cried and beat their chests in mourning.

Most of the victims lived nearby, and funeral prayers were expected to be held later on Tuesday.

Grief was accompanied by anger as residents demanded stern punishment for the owner of the tutoring centre, accusing him of running classes in what they described as an ageing and unsafe building. Dozens of mourners gathered outside the victims' homes to offer condolences.

"We don't know whose home to visit first to offer condolences for the loss of their children," resident Zafar Iqbal said as he moved from one bereaved family's home to another nearby.

Lahore is the capital of Pakistan's most populous province, Punjab, where many parents send their children to private tutoring centres in the afternoons and evenings.

Pakistan's President Asif Ali Zardari and Prime Minister Shehbaz Sharif expressed grief over the tragedy. In separate statements, they offered condolences to the bereaved families, prayed for the speedy recovery of the injured, and stressed the need for effective safety measures to prevent similar incidents in the future.