Ahmed, in Cairo for talks with Egyptian President Hosni Mubarak, warned against US military action against the pirates.
"We advise against resorting to (US military strikes) and rather to focus on finding a comprehensive solution," he said, adding that Somalia's piracy was the result of the loss of "security and stability" in his country.
The new US administration has pledged to step up the fight against pirates from Somalia after a US cargo ship was seized earlier this month.
"The pirates live on land... and therefore confronting them begins where they live, and that can be achieved through strengthening the abilities of Somalia's police," Ahmed said.
He said that under the Islamic Courts, the Islamist movement which controlled the government in Mogadishu from 2006 until it was ousted a year later by Ethiopian troops, the pirates had been "finished off."
Ahmed, a former Islamist rebel leader, was elected in January and agreed in February to proposals by leaders mediating between his government and Islamic hardliners for a truce and the implementation of Islamic sharia law.
The government has not yet been able to counter the pirates, who increased their attacks tenfold in the first three months of 2009, compared with the same period last year, according to the International Maritime Bureau's Piracy Reporting Centre.
Ahmed will on Thursday attend a one-day donors conference in Brussels, where the European Commission has said it will pledge at least 60 million euros (78 million dollars) to help boost security in war-torn Somalia.
The European Union's executive arm said the money would be used "to support Somalia's security institutions and the African Union (peacekeeping) Mission in Somalia (AMISOM)."
Somalia has had no effective central authority since the 1991 ouster of president Mohamed Siad Barre touched off a bloody cycle of clashes between rival factions.
