Hundreds of people fleeing the attack are arriving by boat in the port city of Pemba, a diplomat and an aid worker said.
Militants struck Palma, a logistics hub for international gas projects worth $A79 billion, on Wednesday.
The government has yet to re-establish control, the diplomat and a security source directly involved in the operations to secure Palma said.
Reuters could not independently verify the accounts as most communications with Palma were cut on Wednesday.
Calls to officials at the foreign ministry and provincial government went unanswered or did not go through on Sunday.
The government has said it is working to restore order in Palma.
The boats arriving in Pemba on Sunday carried both locals and foreigners, including employees from the gas projects, the aid official and diplomat said.
One boat was carrying about 1300 people, the diplomat said.
French energy group Total said on Saturday it was calling off a planned resumption of construction at its $US20 billion development following the attack and would reduce its workforce to a "strict minimum".
The company pulled out the majority of its workforce in January due to insecurity in Cabo Delgado province, which has been the target of an Islamist insurgency since 2017.
Witnesses have described bodies in the streets of Palma, some of them beheaded.
On Friday, militants ambushed a convoy of people including foreign workers attempting to escape a hotel.
A South African woman, Meryl Knox, told Reuters that her son Adrian Nel died in the attack.
Her husband and another son hid with his body in the bush until the following morning when they were able to make it to safety in Pemba, she said.
She did not have further details.
Government-contracted helicopters were searching for more survivors.
Lionel Dyck, who runs a private security firm working with the government, said his helicopters had rescued at least 17 people on Sunday.
The number of people injured and killed in the four-day assault on Palma, or still unaccounted for, remained unclear.
The town had previously been a refuge for people fleeing violence elsewhere in the province.