Karzai asked Adm. Mike Mullen, the chairman of the Joint Chiefs of Staff, what kinds of operations the newly deployed troops would carry out and said the Afghan government should be consulted about those operations.
Mullen over the weekend announced that the U.S. would send an additional 20,000 to 30,000 troops to Afghanistan by summer, reflecting the deteriorating security situation around the country more than seven years after the U.S. invasion.
Karzai's office said in a statement that Mullen told the president the new troops would be sent to dangerous regions with little security, particularly along the Pakistan border. Mullen on Saturday told reporters that NATO and the U.S. have "enough forces to be successful in combat, but we haven't had enough forces to hold the territory that we clear."
The Afghan president also told Mullen that the troops need to be careful in Afghan villages. Karzai has long decried the civilian casualties caused by some military operations.
Elsewhere, a joint U.S.-Afghan operation along the border with Pakistan has killed about 20 insurgent fighters over the last month, an Afghan governor said.
The Afghan and U.S. forces taking part in Operation Lion Heart are trying pressure militants along the border between Afghanistan's Kunar province and the Bajur region in Pakistan.
Pakistani forces are conducting their own operation in Bajur in coordination with the U.S. and Afghan forces.
The Ministry of Defense said Monday that dozens of militants have been killed and wounded over the last month. A spokesman said he couldn't give more precise numbers.
However, Kunar Gov. Sayed Fazeullah Wahidi said around 20 fighters have been killed over the last month, including two Arabs and two Pakistanis.
Foreign militants from Uzbekistan, Chechnya and Arab countries have joined the fight with Taliban militants who operate in the Afghan-Pakistan border region. Al-Qaida fighters also operate along the border.
Meanwhile, a car bomb with two attackers exploded Monday near an Afghan governor's compound, killing one Afghan civilian and wounding seven. The two attackers also died, said Sayed Ismail Jahangir, the spokesman for the governor of Ghazni province in central Afghanistan.
Shops around the governor's compound were damaged, and shattered glass littered the ground around the bombing.
Violence has spiked around Afghanistan the last two years. More than 6,100 people have died in insurgency related violence this year, according to an Associated Press count of figures from Afghan and Western officials.