Thousands of US troops are in Afghanistan
"We have a commitment to free our country and the rest of the world from this scourge of terrorism and we will see to it that it is completed by whatever means," he said.
Mr Karzai said that although the Taleban regime - which harboured Osama Bin Laden's al-Qaeda terror network, suspected of carrying out the 11 September attacks on the US - had been toppled, there were still some rogue fighters holding out in parts of the country.
"Generally the Taleban movement or that regime has completely
gone away from Afghanistan. The main terrorist bases associated with
them have been removed," he said.
"There may be individuals hiding in parts of Afghanistan. We are looking for them. In recent days some have been arrested and we are looking for more.
"We will see to it that terrorism is completely finished in Afghanistan in all its forms."
In other developments:
Mr Karzai's comments followed the first meeting of the country's new government in the capital, Kabul, focusing on restoring security to the war-ravaged country.
All 30 members attended the session, which also discussed ways of reviving or setting up a functioning administration.
Mr Karzai, who was sworn in as leader on Saturday, has said his government faces political oblivion unless it can succeed in bringing peace and stability to the country.
He has appealed for billions of dollars in international aid.
The BBC's Richard Miron says Mr Karzai's administration has popular backing for the moment at least.
Convoy allegations
Mr Karzai has also said he will investigate reports that US aircraft killed civilians when they bombed a convoy in eastern Afghanistan last week.
The US military continues to maintain that the convoy was a "valid" Taleban or al-Qaeda target that opened fire on its warplanes.
This is despite survivors and
witnesses saying that it was carrying tribal elders to Kabul for Mr Karzai's swearing-in as the new Afghan leader.
Residents of Asmani Kilai in eastern Paktia province said the strikes, lasting seven hours from Thursday night into Friday, killed 50 to 60 people and destroyed 15 vehicles.
Haji Yaqub Khan Tanaiwal, 65, told Reuters news agency from his hospital bed in Peshawar, over the border in Pakistan, that no one in the convoy had fired on US warplanes.
"All in the convoy were supporters of the new administration," he said.
"There were no al-Qaeda people or Taleban."
Local tribal leader Gulab Din has threatened to launch a war against the new Afghan administration if US warplanes carry out further attacks on targets in his area of Paktia province, according to the Pakistan-based Afghan Islamic Press.
"If the US launches similar tyrannical attacks again, we will launch an armed struggle against Hamid Karzai's government," he told AIP.