The chief secretary directed the deputy commissioners to go for complete lockdown in such areas for containment of the disease and ensure that there is zero movement of people, they added.
The total number of positive cases in the union territory has risen to 245 — out of which 197 were in Kashmir and 48 in Jammu.
While four patients have died in Jammu and Kashmir, six have recovered.
More than 51,000 people have been kept under surveillance including those who are either in government established quarantine facilities or in home isolation.
Till date, 51320 travellers and persons in contact with suspected cases have been put under surveillance which include 9153 persons in home quarantine including facilities operated by government, 433 in hospital quarantine, 235 in hospital isolation and 29718 under home surveillance. Besides, 11777 persons have completed their 28-day surveillance period,” the officials said.
They said the union territory has ramped up testing and was now testing at the rate of 289 persons per one million of the population.
Over 400 persons tested on Sunday alone. This may lead to more positive cases or declaration of more areas as red zones, but it is not a cause for alarm, the officials said.
Meanwhile, markets across the valley were shut and public transport was off the roads with only pharmacies and groceries allowed to open, the officials said.
Educational institutions across Kashmir are closed, while all public places including gymnasiums, parks, clubs and restaurants were shut down more than a week before the nationwide lock down announced by Prime Minister Narendra Modi.
While the Prime Minister announced the country-wide lockdown on the evening of March 24, the union territory administration here had on March 22 announced a lockdown across Jammu and Kashmir till 31 March as part of its efforts to curb the spread of the coronavirus.
The administration said the essential services including healthcare personnel have been exempted from the restrictions.
Restrictions were first imposed in many parts of the valley on March 19 to contain the spread of the virus. The measures were taken after the detection of the first positive case of coronavirus in the valley.