Allen said that the drawdown of US forces that started earlier this month and the transition of some areas to Afghan control this week does not mean that international forces are easing up in their campaign to defeat the Taliban insurgency.
"It is my intention to maintain the momentum of the campaign," Allen said at the handover ceremony in the Afghan capital. He said however, that he does not expect the fight to be easy.
"There will be tough days ahead. I have no illusions about the challenges ahead," he said.
US officials have trumpeted success in reclaiming Taliban strongholds in southern Afghanistan and training Afghan security forces as signs that they are finally making progress toward peace in Afghanistan. But violent attacks have continued, including a number of high-profile assaults and assassinations in recent weeks.
Today morning, a bomb killed three international service members in the east, NATO said in a statement. It did not provide nationalities or further details. Most of the troops in the east are American.
At least 37 international forces have been killed so far this month in Afghanistan.
Allen, who was promoted to a four-star general shortly before the handover ceremony, takes over from Petraeus, who commanded international forces in Afghanistan for one year and is retiring from the military to become the director of the Central Intelligence Agency.
The ceremony came just hours after security forces in the capital killed the final attacker in the assassination of a close adviser to President Hamid Karzai.