The clearance operations began in the capital and neighbouring provinces two days ago, and will continue, Zabiullah Mujahid said. The aim was to collect weapons and arrest suspects, he said.
“The operation was successful,” Mr Mujahid said.
Hundreds of light and heavy weapons were confiscated, including rocket launchers and grenades, he said.
More than 60,000 rounds of ammunition were uncovered, as well as 13 armoured vehicles and 13 tonnes of gunpowder and explosives.
Mr Mujahid also welcomed a recent US decision to ease restrictions on Afghan banks.
The general licence issued by the US Treasury will allow money transfers for Afghan businessmen and others, but exclude Taliban members.
Mr Mujahid said he hoped the US would continue to ease restrictions.
Billions of dollars of Afghan assets are frozen in US banks, severely hampering state institutions in the once aid-dependent country.
The Taliban said nine kidnappers, six ISIS members and 53 thieves were arrested. Two abducted people were released.
The operations, in which Taliban went door to door, have attracted criticism amid reports of abuse suffered by civilians, including minority groups and women, at the hands of Taliban forces.
“The intimidations, house searches, arrests and violence against members of different ethnic groups and women are crimes and must stop immediately,” tweeted Andreas von Brandt, EU ambassador to Afghanistan.
Mr von Brandt has not returned to the country since the Taliban takeover in August.
Responding to criticism, Mr Mujahid said the operation was “well organised” and included female security personnel.
“All these efforts are for the benefit of the people," he said. "It was necessary for the people and the government to launch such an operation."