Cheney was taken from Kabul International Airport by a U.S. military helicopter to the presidential palace in Kabul where he met with Karzai.
Speaking with Karzai at a press conference after their talks, Cheney said the meeting focused on the existing U.S.-Afghan strategic partnership. He said the two also discussed how their countries will continue to work together in the future to fight terrorism and rebuild Afghanistan.
"I'm here to reaffirm the bonds of friendship and cooperation that define relations between our two countries," Cheney said. "Having led a coalition to remove the former [Taliban] regime, the United States continues to lead the effort to rebuild Afghanistan and to help its people consolidate the gains of democracy."
Cheney emphasized that international forces will remain in Afghanistan for as long as it takes to build the Afghan military and police forces so that they can secure the country on their own.
"The United States and the other members of the coalition need to have a sufficient force here to be able to ensure security to deal with the threat that has been represented by continuing activities by radicals and extremists of the likes of the Taliban and Al-Qaeda," he said. "But ultimately, security in Afghanistan will depend upon the ability of the Afghan people to provide adequate forces that are well trained and well equipped."
President Karzai described Cheney's remarks as "encouraging." But he also said it would take "a long time" before Afghan security institutions are able to do the job without international support.
"We would like an effective continuation of the two missions that we have here," Karzai said. "One is the fight against terrorism. The other is the rebuilding of Afghanistan -- and especially the rebuilding of the security institutions, the army. As it is a gradual improvement on our side, it is also a gradual reduction of responsibility on the shoulders of the international community. But that is not going to be any time soon. Afghanistan will need, for a long time, support from the international community in the rebuilding exercise here in Afghanistan and in the strengthening of the Afghan security institutions."International Support 'A Must'
Karzai also stressed that Afghanistan needs continued help on security not just from the United States, but also from other countries in the NATO alliance.
"In my meetings with the Afghan people, I find out that the army is more and more seen as a force that brings stability," he said. "As the Afghan army gets stronger and stronger, so the pressure will lessen on the international security forces. Until then, the cooperation between Afghanistan and the rest of the international community is a must -- both for the war against terrorism and stability in Afghanistan."
The United States, Canada, and Britain have been calling for other NATO countries to increase their contributions of troops and equipment to Afghanistan. In particular, they want NATO's European allies to deploy combat troops to southern Afghanistan to battle Taliban and Al-Qaeda fighters.
Cheney said Afghanistan is better off by virtue of NATO's presence in the country. But he said the NATO commitment needs to be reinforced.
"When the [U.S.] President [George W. Bush] goes to Bucharest in a couple of weeks to participate in the NATO summit, one of the most important items on the agenda will be the NATO role and mission here in Afghanistan," he said. "I would expect that we will see a reaffirmation and a resumption, if you will -- a renewal -- of the commitment that we have made collectively as an alliance to the independence and freedom of the people of Afghanistan. I'm quite confident, in fact, that NATO will continue to play a major role and hopefully even expand their efforts beyond those that they've already undertaken."
Cheney also said that Pakistan's tribal regions near the border with Afghanistan must be controlled by the country's new government, which is emerging as a result of parliamentary elections there last month.
"We look forward to working with the new government of Pakistan once it is finalized as a result of the elections," Cheney said. "We believe that a government has an obligation to control its sovereign territory to make certain that that territory doesn't become a safe haven or sanctuary for special terrorist groups intending to do harm to others. I would expect that Pakistan will certainly fulfill that obligation in the years ahead. That's important not only to the people of Pakistan but also to others who might be threatened by developments in that area if they are not properly controlled by the sovereign government of Pakistan."
Cheney has already visited Iraq and Oman on his current tour. According to his planned schedule he also plans to visit Saudi Arabia, Israel, the Palestinian territories, and Turkey.RFE/RL's Radio Free Afghanistan correspondents Ahmad Djakfar and Jawad Mujahed contributed to this report from Kabul.