"When (piracy) implies a great risk of being caught and hanged, and the cost of losing ships and weapons becomes too big, it will decrease and eventually disappear," Jacob Stolt-Nielsen said in an op-ed in Norwegian financial newspaper Dagens Naeringsliv.
The 79-year-old is the founder of Stolt-Nielsen Ltd, one of Norway's biggest shipping companies. He stepped down as chairman two years ago but still serves on the board.
"Pirates captured in international waters have always been punished by death, often on the spot," Stolt-Nielsen wrote Tuesday, arguing that modern navies should deal with the problem like Roman pirate hunter Pompey did more than 2,000 years ago.
"Not arrest them and say, 'naughty, naughty, shame on you,' and release them again, but sink their boats with all hands," he wrote. "The pirates won't be frightened by being placed before a civilian court."
The article drew sharp criticism in Norway, a seafaring nation known as a peace broker in many of the world's armed conflicts and as the home of the Nobel Peace Prize.
Jacqueline Smith, president of the Norwegian Seafarers Union, described Stolt-Nielsen's views as "barbaric" and said killing pirates could endanger the 700 seafarers now held as hostages in Somalia.
Piracy in the busy shipping lanes off the African nation has flourished since its government collapsed in 1991.
Erik Lahnstein, state secretary at Norway's Foreign Ministry, said basic human rights must apply also to pirates, and noted that "even for the most gruesome crimes, we do not have death penalty in Norway."
Stolt-Nielsen acknowledged that killing pirates could trigger a backlash against crews held hostage. "But you can't make an omelet without breaking eggs. This is war and warfare costs lives," he wrote.
The company issued a statement emphasizing that the comments in the article reflected "Mr. Jacob Stolt-Nielsen's own personal opinion."
The company's ships have been exposed to pirate attacks off Somalia's coast and some of them now carry armed guards. Other ship owners have taken similar steps to protect their ships and their crews.
Meanwhile, in Somalia, the bodies of eight pirates killed in a commando raid last month on a South Korean freighter were brought to Mogadishu's airport, said Ibrahim Iman, the airport manager. South Korean commandos raided the chemical carrier Samho Jewelry and freed the crew of 21.
Halima Hassan, a sister of one of the dead pirates, said her brother was innocent and was killed as he was guarding the coast "from illegal fishing vessels."
Piracy attacks off Somalia began in retaliation for illegal shipping off the coast, though the piracy industry has evolved into a multimillion dollar business with near daily attacks.
AP reporters Mohamed Sheikh Nor in Mogadishu, Somalia, and Hyung-Jin Kim in Seoul, South Korea, contributed to this report.