The directions were given at a review meeting chaired by the chief minister, in which he took note of the low vaccination numbers in the state.
According to an official statement, he expressed concern that of 1,291 registered private facilities, 891 have reportedly not administered a single dose.
He asked the district administration to come down heavily on such hospitals, stressing that private health facilities need to join the government battle against coronavirus.
Charges for a coronavirus vaccine in private health care institutions must be publicised and overcharging should not be permitted, he directed the Health Department.
He asked all elected and local leaders to make efforts to reach out to the public and address vaccination hesitancy.
The CM directed the Health Department to ensure the coverage of all frontline workers. This must include all those who provided essential services or were on COVID duty during the curfew and the lockdown, he added.
The chief minister said the state has consistently remained at the 18th position among all states in India in terms of the COVID numbers.
Though the death rate has been a matter of concern, at 206 deaths per million population, Punjab compares well against Delhi at 542 and Maharashtra at 431, he added.
However, it is a matter of concern, said the chief minister, that after bringing the problem under control by the end of the last year, the state is again seeing a surge for the last one month.
From a low of around 200 cases daily and deaths in single digits, Punjab has gone to around 2,000 cases per day and the deaths are also increasing, he noted.
We have to be prepared for this second surge, said Amarinder, pointing out that the 1918 Spanish flu had four spikes. We have to be prepared for a long battle, he warned.
The chief minister, however, said his government is fully prepared to deal with the second wave.
In the meeting, Deputy Commissioner Jalandhar said the district administration was making it mandatory for chemists and private practitioners to report people who come for treatment with flu symptoms.
He urged the chief minister to empower the Transport Department to issue challans in case of mask violation.
Pointing to five per cent positivity rate in the district this month, the Patiala deputy commissioner said more cases were being reported from the Patiala civic body area.
The district administration will increase sampling to 4,000 a day in the next couple of days, he said, adding that the next two weeks are critical.
DCs of Mohali and other districts also updated the chief minister on the situation as well as the measures being taken to check the coronavirus spread.