The toll from Dominica brings the overall number of confirmed deaths caused by Hurricane Maria to 18, including two in Guadeloupe and one in Puerto Rico.
"So far, we would have buried in excess of 15 people," Skerrit told a television network of Antigua and Barbuda, a neighboring country.
"If there (are) no other fatalities, it is a miracle," he said.
The hurricane devastated the island, which has some 72,000 inhabitants and was hit by the storm on September 18 when it was at the height of its Category Five power.
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Now, "we have no water, no electricity, very limited communications," Skerrit said.
"The main hospital is functioning without electricity. It is very difficult. There are no generators, they have been set aside because of the flooding," he said.
Dominica, which is located near the French islands of Martinique and Guadeloupe, has been almost completely cut off from the world.
Helicopter support is needed to airlift in supplies, with immediate needs ranging from food for babies and hygiene kits to generators and construction materials, the premier said.