Earlier unconfirmed reports said the defendants all came from the Yemeni city of Lahij and had been veterans of the anti-Soviet, Islamic resistance in Afghanistan in the 1980s.
Speaking in an interview with Associated Press, Abdul Karim al-Iryani said there was "no question" the men were involved in the attack, which killed 17 seamen and nearly sunk the vessel in Aden harbour.
Earlier unconfirmed reports said the defendants all came from the Yemeni city of Lahij and had been veterans of the anti-Soviet, Islamic resistance in Afghanistan in the 1980s.
This was confirmed by the prime minister who said the plot also involved "international terrorist elements... I mean Arab-Afghans, not exclusively Yemeni preparation and execution".
Yemeni authorities have detained a number of people since the 12 October attack.
'No question'
Mr Iryani said the three were all "culprits in preparing for the attack on the Cole" but he had no details on their exact roles or the charges they would face.
Unconfirmed reports on Monday said two were accused of involvement in organising the attack, while others were described as junior employees in the Lahij civil records office accused of having abetted the perpetrators and helped them obtain forged identity cards.
Mr Iryani said the suicide bombers themselves were too young to have fought in Afghanistan, but it was possible some of the other suspects were Afghan veterans.
US suspicions
Washington says it believes the attack was instigated by, among others, the Saudi fugitive Osama bin Laden, himself a veteran of the Afghan war, who now lives in Afghanistan under the protection of the Taleban Government.
However, Mr Iryani said Yemen had not yet produced any leads identifying outside perpetrators.
The ship is currently crossing the Atlantic on a Norwegian dry-dock vessel and is due to arrive in the US next week for extensive repairs.
The repairs due to begin in Mississippi in January are expected to take more than a year and will cost more than $100 million.