Two Chinese nursery school pupils have died after drinking yoghurt laced with rat poison, apparently because the head of a rival institution hoped to damage the reputation of their school, police have told state media.

Officers said the main suspect, Shi Haixia, 39, admitted injecting the bottle with tetramine and asking Yang Wenming, 51, to leave it on the street near her competitor's business, along with school supplies.

She feared that the other school was enrolling more students, in Lianghe village in Pingshan county, in the northern province of Hebei, officers told the Global Times.

The bag was spotted by the victims' grandmother, Ren Shuting, who took it home. The five- and six-year-old girls began foaming at the mouth and convulsing after drinking the yoghurt. One died on her way to hospital; the other died on Wednesday, after a week of treatment. Ren, who also took a sip of the liquid, was admitted to hospital.

The case came less than a fortnight after authorities in Kaixin county, Chongqing, blamed rat poison for the illness of more than 100 nursery school pupils. Chongqing's propaganda office said it had no more information on that case and Kaixin officials did not answer calls.

Many in China have blamed the latest case on the vicious competition between nursery schools, which has led to owners employing increasingly aggressive tactics to win pupils.

But there have also been a number of chilling poisonings in the country in the past, often linked to disputes. In a notorious incident in 2002, two teachers and 70 children at a nursery in Guangdong became seriously ill after the head of a rival institution blamed it for the failure of his business and put rat poison into the table salt. The man, Huang Hu, was later executed.

The following year, 38 people died and hundreds were made ill after a snack-shop owner poisoned a competitor's food. Another 10 were killed when a widow spiked the meal at her husband's funeral over a family dispute. In a third case, a man sought revenge against his married lover as their relationship turned sour by poisoning her children's snacks. One of the children, and a classmate with whom he shared the food, died; 25 other pupils were taken ill.

China tightened its laws on the use of tetramine, warning that those who produced and sold it illegally could face punishments including the death penalty. But in 2007 rat poison killed one person and left hundreds ill in Harbin after it ended up in breakfasts served at a local hospital.

Two years later a nursery pupil in Guangxi Zhuang Autonomous Region died and 20 others were admitted to hospital in similar circumstances.

And in 2011 a sex shop owner in Hebei province attacked a competitor by leaving a tetramine-tainted snack in his store. His rival was taken seriously ill and the suspect tried to mislead detectives by leaving out other poisoned food, causing the deaths of three boys aged between two and 17.

Tan Fang, a professor at South China Normal University and founder of the Chinahaoren website, which aims to promote civic responsibility, warned: "This incident exposes the serious decline in our country's morality and the loopholes in the judicial safeguards that people rely on. China boasts of having the traditional morality of 'respecting the old and cherishing children'. Children don't hurt economic interests, or political interests, but criminals will even commit crimes against children."

He said that while children needed to be better protected, the deeper issue was China's changing values. Society and spiritual civilisation had been damaged by the cultural revolution and then by the extremes of the market economy, he added. The party had also handled some problems inappropriately.

In some of the poisoning cases the offenders may not have anticipated how serious the results would be. In 2009, police in Kunming said a 12-year-old victim of bullying who poisoned 10 classmates had believed they would suffer only diarrhoea. The victims all survived.

Accidental poisonings have also claimed lives. Last month one person died and 20 were taken ill after a chef mistakenly added pesticide to the lunch he was preparing instead of sauce, the Xinhua state news agency reported.