Spanta told a Kabul press conference that international terrorism stemming from religious extremism is the work of a global network operating against Afghanistan and other democratic states from the United States to Russia and India.
He indirectly suggested Pakistani involvement when he said one country is helping that network.
Spanta was responding to a claim by Pakistan's President Pervez Musharraf last month that Taliban insurgents had roots among Afghanistan's Pashtun tribes.
Afghan and international officials say radical groups in Pakistan support the Taliban in their increasingly bloody insurgency against the Afghan government.
The ousted Taliban came to power in 1996 with the support of Pakistan, which was one of only three nations to recognize their government.
This year has seen an upsurge of violence in Afghanistan, particularly in the south of the country.
The latest casualties include two Canadian soldiers killed in an ambush on 14 October. Two others were wounded, Canadian officials say the soldiers were operating in the Panjwayi district of Kandahar Province when they came uner attack. Other Canadian units who responded to the attack battled insurgents for three hours.
Canada has now had 42 soldiers and one diplomat killed in Afghanistan since 2002.
Meanwhile, a bomb blast in the western Afghan province of Herat on October 15 killed two civilians and wounded another. A provincial official says the remote-controlled blast was apparently aimed at U.S. police trainers whose vehicle was passing at the time. The two civilians killed were riding bicycles nearby.