Security has been increased at schools following the spate of attacks
China's Premier Wen Jiabao has said a spate of fatal attacks on schools shows the country has "social tensions" which must be addressed.
Wen Jiabao's comments, to a Hong Kong television channel, are the most direct official remarks on the violence.
At least 17 people, mostly children, have been killed and dozens injured in a series of apparently random bloody attacks in the past two months.
Officials have ordered an increase in security at schools and nurseries.
But Mr Wen said that as well as boosting the security presence, China needed to "handle social problems, resolve disputes and strengthen mediation at the grassroots level".
There has been much speculation in China that inadequate understanding of mental health issues and a lack of official outlets to air grievances has contributed to the violent outbursts recently seen.
China's minister in charge of public security, Wu Heping, said the crimes deserved "the outrage of all Chinese people".
"The public security bureaus and judicial authorities will severely punish this kind of crimes according to law," he told reporters.
THIS YEAR'S ATTACKS
12 May: Seven children and two adults killed and 11 hurt in Hanzhong, Shaanxi province
30 April: Five children hurt in hammer attack in Weifang, Shandong
29 April: Three adults and 28 children injured in Taixing, Jiangsu
28 April: At least 15 children and one teacher injured in Leizhou, Guangdong
24 March: Eight children killed in Nanping, Fujian
But Mr Wu also said society was changing rapidly and that subsequent changes in policy were be needed.
"Innovation in the management of society is not only essential but urgent," he said.
"I have noticed the central government's demand for the public security bureaus, under the leadership of all levels of local government, to properly handle the various conflicts in society."
There have been at least five violent attacks on schools and nurseries in China in recent months, mostly carried out by unemployed local men.
In the latest attack, on Wednesday, seven children - the youngest three years old - and two adults were killed by a man wielding a meat cleaver at a kindergarten in Hanzhong city, Shaanxi province.
The attacker, Wu Huanming, was described as quiet and unremarkable by his neighbours.
He was reported to have owned the building in which the privately-run kindergarten was held and to have been involved in a rental dispute with its manager, Wu Hongying.
She and her mother were both killed and Mr Wu, who was not thought to be related, later killed himself.
Li Zhenfeng, a deputy police chief in Hanzhong, said Mr Wu had also been suffering from depression linked to worsening physical illnesses.
"With these factors combined, Wu Huanming decided to take his revenge against others and commit suicide, and he directed his hatred toward Wu Hongying," said Mr Li.
Correspondents say China has in the past had a comparatively low rate of violent crime, meaning the recent violence has been all the more shocking.