"The operation is ... unfolding positively. It's giving us reason to hope for success," Rogozin said.
The Finnish-owned Arctic Sea, which its owners said was carrying timber, set sail from Finland on July 23 headed for Algeria. The next day, the crew reported, about a dozen men boarded the ship near the Swedish island of Gotland, tied up the crew, beat them, said they were looking for drugs and then sped off in an inflatable craft.
The ship continued its journey but disappeared last month after passing through the English Channel.
The French Navy on Saturday said the ship was most likely near Cape Verde, off West Africa. Finnish authorities reported that the ship's owners had received a ransom demand, but they gave no further details.
Viktor Matveyev, director of operator Solchart Archangelsk, did not answer calls to his mobile phone on Sunday.
Nick Davis, a British maritime security expert with the Merchant Maritime Warfare Center, said he believed the ship was probably off Africa's coast, possibly near Sierra Leone or Cameroon.
"If it's a bona fide ransom that's been demanded, that would lead me to believe the vessel is at its safe destination where the hijackers feel they are able to extort money," Davis said.
Davis also said he thought the ship's disappearance appeared to be a well-planned hijack and was likely the result of a commercial dispute, rather than the sort of opportunistic piracy carried out by pirates off Africa's east coast.