Karzai also called on the international community to reassess its approach to the war on terror, saying the deaths of hundreds of Afghans, including Taliban militants, in fighting with U.S.-led forces was "not acceptable."
The posting of Ayman al-Zawahri's videotape on an Islamic Web site followed a coalition military warning Wednesday that "significant violence" lies ahead in southern Afghanistan, where thousands of troops are fighting a deadly Taliban resurgence.
The taped message was al-Zawahri's sixth this year and posted on a Web site known as a clearing house for al Qaeda and other militants' statements.
"I am calling upon the Muslims in Kabul in particular and in all Afghanistan in general and for the sake of God to stand up in an honest stand in the face of the infidel forces that are invading Muslim lands," said al-Zawahri, wearing a white turban and sitting in front of a black backdrop with an automatic rifle next to him.
The Egyptian-born fugitive also called on "the young men of Islam, in the universities and schools of Kabul, to carry out their duties in defense of their religion, honor, land and country."
The 3 ½ minute tape, entitled "American Crimes in Kabul," appears to have been made the day after a May 29 accident in which a U.S. military truck crashed into traffic in Kabul, killing up to five people. The incident sparked anti-foreigner riots in Kabul that left about 20 people dead, the deadliest unrest here since the Taliban's 2001 ouster.
"I direct my speech today to my Muslim brothers in Kabul who lived the bitter events yesterday and saw by their own eyes a new proof of the criminal acts of the American forces against the Afghani people," al-Zawahri said on the videotape.
Unlike al-Zawahri's previous messages, which appeared aimed at Americans, the latest video has no English subtitles. He spoke in Arabic, and Web sites carried translations in Pashtun and Farsi, two languages widely spoken in Afghanistan.
Asked about the new tape, Karzai blamed al-Zawahri for Afghanistan's massive suffering before and after the Sept. 11, 2001, attacks.
"He is first the enemy of the Afghan people, and then the enemy of the rest of the world," Karzai said during a press conference. "He killed Afghans for years, thousands, and then he went to America and destroyed the twin towers."
"We in Afghanistan want him arrested and put before justice."
A clearly frustrated Karzai also said the coalition approach of hunting down militants does not focus on the roots of terrorism itself.
"I strongly believe ... that we must engage strategically in disarming terrorism by stopping their sources of supply of money, training, equipment and motivation," Karzai said.
More than 600 people, mostly militants, have been killed in recent weeks as insurgents launched their deadliest campaign of violence in years. CBS News correspondent Mark Phillips notes that more than 1,000 people, including 40 foreign troops, have died this year.
"It is not acceptable for us that in all this fighting, Afghans are dying. In the last three to four weeks, 500 to 600 Afghans were killed. (Even) if they are Taliban, they are sons of this land," he said.
Coalition and Afghan forces launched Operation Mountain Thrust in earnest last week with more than 10,000 Afghan, British, Canadian and American troops deploying in the largest anti-Taliban offensive since the former regime's 2001 ouster.
In renewed violence, Afghan and coalition forces raided a Taliban compound Thursday in southern Afghanistan, killing eight insurgents, the military said. The raid took place at a "known enemy compound" northwest of Tirin Kot, the capital of Uruzgan province, a military statement said. Another six militants were captured and detained for questioning, the military said.
Four U.S. soldiers were killed and another wounded Wednesday while trying to block the movement of enemy forces in the eastern Nuristan province, the military announced in a statement Thursday.
Ground troops and attack planes were called in to continue the assault through the night, but it was unclear if there were any enemy casualties.
Afghan and coalition forces have been targeting al Qaeda and Taliban militants along the Pakistan border since mid-April.
Late Wednesday, militants bombed two coalition convoys in southern Afghanistan, killing one civilian bystander and wounding 13, including six Canadian soldiers, the military said.
Al-Zawahri and al Qaeda leader Osama bin Laden were hosted by the Taliban before their ouster. They both are now believed to be hiding in the rugged border frontier between Afghanistan and Pakistan.