Emergency provisions issued on Friday include restricting all public gatherings in the country to no more than five people.
Public transport carrying more than five people is to be temporarily halted and nightclubs, restaurants and cinemas are to be closed.
Street vendors have been told to not operate and people aged over 60 have been told to remain at home unless seeking medical attention.
Travel to the island of Savai'i has been limited to just three days a week. Non-essential public servants are also having their hours reduced.
But the ban on public gatherings of more than five people is being openly flouted.
Fuiavailili Egon Keil said police received a number of calls from members of the public about several church parishes carrying out services despite the restrictions.
It was surprising that some people might not be complying with the orders, he said.
"So, we're urging our religious sector to please conform. We've talked to the National Council of Churches. We've talked to the heads of different church organisations, and they're all aware of our position here."
The commissioner said people could face a fine of $US4,500 (10,000 Samoan Tala) or sentenced to two years in jail for the violation of orders in a state of emergency.
Mr Keil said arrests were a last resort, but police had already made at least one arrest so far - a street vendor who continued to sell goods in front of a shop in town.
"Our last resort is making that arrest, which we do not want to do.
"What we're trying to get is volunteer compliance, and that we all work together on this. We're trying to deal with the spirit of the law, not the letter of the law," he said.
Police have issued 120 warnings as of Sunday due to non-compliance.
Photo file Caption: Samoa Police Commissioner Fuiavailili Egon Keil