The family has been moved to a larger ship, and none of the hostages has been harmed, a pirate said.
Later Wednesday, the Danish government said it had established contact with the pirates and their hostages.
"They are doing well under the circumstances," the Foreign Ministry said in a brief statement.
It said a professional security firm was handling negotiations with the pirates, declining to give more details, citing concern for the hostages and their relatives. The statement did not mention anything about a ransom.
A Somali pirate previously warned that if any attempt was made to rescue them, they would meet the same fate as the four American yachters slain by their pirate captors last week. Any chance of a quick rescue seemed to disappear Wednesday.
The sailboat being piloted by Jan Quist Johansen, his wife and their three children, ages 12 to 16, anchored near the coastal village of Hafun late Tuesday, said Yusuf Abdullahi Sanyare, the commissioner of Hafun, which lies on Somalia's northern tip, in a region known as Puntland.
Abdiaziz Mohamud Yusuf, the spokesman for a community group called the Puntland Peacemakers, told The Associated Press that the family has been taken on land.
However, a Somali pirate who gave his name as Muse Abdi said the family was transferred to another, larger pirated ship. He said the family has not been harmed.
"They are safe. They were just transferred from the boat to the big ship," said Abdi, who has provided reliable information in the past. "They have been added to other nationals in another ship to avoid any possible attack."
Denmark says it has established contact with the pirates who captured a Danish yacht in the Indian Ocean and with the Danish family that was taken hostage.
Two adult Danish crew members were also seized in the attack last Thursday on the Johansens' 43-foot sailboat.
Abdi said that no ransom demands have yet been made. He said the pirates aren't criminals but "coast guards." The Somali piracy scourge began when fisherman several years ago tried to scare off international trawlers fishing Somalia's waters.
That trend turned into the modern-day piracy machine. Pirates today hold at least 660 hostages from around 30 ships. The average ransom paid to release a ship and crew has reached close to $5 million.
The Johansen family was aware of the pirate threat in the waters off East Africa, but believed that warships patrolling the waters would protect them, according to entries on their travel blog.
Maritime experts said the Johansens had placed themselves in grave danger off Somalia's lawless coast despite warnings from naval forces struggling to police the area against pirates.
Yusuf, who said he has been contacted by a Danish official in Nairobi, said pirates moved the hostages from the sailboat because of a rumor that a warship was heading to the scene. Yusuf's group has been involved in anti-piracy campaigns.
"We are ready to play our role in the safe release of the innocent family," he said. "We strongly condemn the hijacking of ships and innocent people off Somali waters."
Hostages are held in hot, austere conditions in Somalia — typically for many months — before a ransom is agreed on and paid, and the hijacked ships and crew are released.
Last year a British sailing couple were released after 388 days in captivity. Reports indicated that a ransom in the region of $1 million was paid for their release.
Somalia hasn't had a functioning government since 1991, one of the reasons the piracy trade has flourished.
Abdirizak Ahmed, who heads the anti-piracy program in Puntland, Somalia's semiautonomous northern region, where most pirates are based, was attending a two-day workshop in Denmark this week on the legal aspects of prosecuting pirates.
"On behalf of the Puntland state of Somalia, I want to say that we are very sad about the situation," said Ahmed. "In order to save these people, let us wait. Any action, including military action and we have seen what happened to the American couple a couple of days ago, we don't want that to happen again. ... Let us wait, let us wait, please."
Associated Press writer Jan M. Olsen in Copenhagen, Denmark contributed to this report.
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