"Attacks by pirates in waters off Somalia are a threat to the international community including Japan, and it is the issue we have to address with urgency," Aso told the Japanese parliament.
Japan is currently limited by its post-war constitution, which tightly restricts the county's military activities abroad.
Tokyo's plans are to send its warships under an existing national law, which enables the navy to use force only to protect Japanese ships or those carrying Japanese passengers or cargo.
The government is already considering a new legislation that would allow its navy to use weapons beyond self-defence and protect non-Japanese vessels.
"The defence ministry believes it is necessary for work on the new law to be speeded up and we will put our efforts into that," Yasukazu Hamada, the country's defence minister, said.
But opposition parties, which control the upper house in parliament, are still divided on the new legislation and may not back the initiative.
Japanese ships could be deployed in the region by March, after Aso issues the final orders.