An explosion was heard in the Afghan capital shortly after Mullen’s arrival but Nato officials say that it was an accident and that there were no casualties.
An anti-personnel mine detonated in an Afghan army vehicle, they say. The driver has been detained for questioning.
Mullen promised Karzai that international troops will "spare no efforts avoiding civilian casualties" and increase cooperation with the Afghan army, a statement said.
Karzai's office said that he welcomed the appointment of General David Petraeus as commander of the International Security Assistance Force (Isaf).
Ahead of the meeting Mullen said he would explain the reasons for McChrystal’s departure - despite widespread reporting of the details of the affair - and assure Karzai that there will be strategic continuity.
“My message will be clear,” he told a press conference in Washington before his departure. “Nothing changes about our strategy. Nothing changes about our mission.”
The military boss was also scheduled to meet the Afghan defence minister, US and Nato officials. He later travelled on to Pakistan, where he will meet President Asif Ali Zardari and military leaders.
British Prime Minister David Cameron said on Friday that his country’s troops should have left the country before 2015.
Nato announced the death of three of its soldiers in a bomb attack in the south on Saturday. The force also said that it had killed a Taliban commander in Logar province.
With 87 foreign soldiers, June has become the most deadly month for the international forces since the 2001 invasion. The death brings the total to 307, compared to 520 for all of 2009.
In London, Mines Minister Wahidullah Shahrani promised total transparency in awarding contracts for the vast mineral wealth whose existence has recently been made public, despite widely reported corruption in the country and the ministry, which led his predecessor to resign.
“After 15 years, the revenue of the government treasury should be 3.5 billion dollars [2.8 billion euros] each year,” he said, predicting that Afghanistan’s reliance on aid would be over thanks to the income.