There has been huge speculation over the reason for the ship's disappearance, ranging from pirates to a mafia dispute to a commercial quarrel.
The matter is being jointly investigated by Finnish, Maltese and Swedish police.
Radar contact with the Arctic Sea was lost after it left the English Channel
A Finnish police spokesman, Mikko Paatero, said that he was unable at this stage to say whether the ransom demand made to the ship's owners, Solchart Management, was genuine.
"The police cannot really speculate," he said. "We need to base our investigation on existing criminal reports, and in this case there are reports of hijacking and aggravated blackmail."
Markku Ranta-Aho, of the National Bureau of Investigation, told Finland's YLE national radio that the demand was for "a largish amount of money".
He said he would not give further details or say where the ship might be located for fear of endangering the crew.
Cape Verde officials say they think the ship is 400 nautical miles (740km) off one of the islands.
But the Russian ambassador to Cape Verde, Alexander Karpushin, said he had not been officially informed of any sighting and told Russia's RAI news agency the information was "not true".
A source linked to the Cape Verde coastguard told AFP news agency the Arctic Sea was outside its territorial waters.
The coastguard was informing maritime officials about the ship's movements, the source said, adding: "When the ship enters our jurisdiction, we will decide in consultation with our partners what actions to take."
Some reports have put the ship 400 nautical miles north of the Cape Verdean island of Sao Vicente.
French intelligence said it had found a ship matching the Arctic Sea's description in the area. The Portuguese military would not confirm one of its planes had flown over the vessel.
Last known contact
Carrying timber reportedly worth $1.8m (£1.1m), the Arctic Sea sailed from Finland and had been scheduled to dock in the Algerian port of Bejaia on 4 August.
It would seem that these acts, such as they have been reported, have nothing in common with 'traditional' acts of piracy or armed robbery at sea
The crew reported being boarded by up to 10 armed men as the ship sailed through the Baltic Sea on 24 July, but the intruders were reported to have left the vessel on an inflatable boat after 12 hours.
There are also reports of the ship being attacked a second time off the Portuguese coast. However the ship's operators said they had no knowledge of the incident and Portugal said the ship was never in its territorial waters.
The last known contact with the crew was when the Arctic Sea reported to British maritime authorities as it passed through the Dover Strait.
On Friday, European Union Commission spokesman Martin Selmayr said: "From information currently available it would seem that these acts, such as they have been reported, have nothing in common with 'traditional' acts of piracy or armed robbery at sea."
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