Afghan president Hamid Karzai has told US Defence Secretary Leon Panetta that Nato troops should pull back to their bases and Afghan forces should take over the lead security role in 2013.
At the same time, the Taliban announced that it was suspending talks with the US amid a series of failed negotiations.
Zabiullah Mujahid, the Taliban spokesman said: "Because of these American changes, the Taliban was obliged to stop the talks."
The move by Karzai follows a week of tension between coalition forces and Afghan locals after the massacre of 16 people, including several children, allegedly by a US soldier in Kandahar at the weekend.
"Afghan security forces have the ability to keep the security in rural areas and in villages on their own," the president said in the statement, following a meeting with Panetta on Thursday.
On the killing in Kandahar, Karzai said that "all efforts have to be done to avoid such incident in the future".
Following the meeting, Panetta said: "I assured him [Karzai] first and foremost that I shared his regrets about what took place. I again pledged to him that we are proceeding with a full investigation here and that we will bring the individual involved to justice. He accepted that."
Shortly after the meeting finished, the Taliban released a statement accusing the US of "wasting time".
"The Islamic Emirate has decided to suspend all talks with Americans taking place in Qatar... until the Americans clarify their stance on the issues concerned and until they show willingness in carrying out their promises instead of wasting time," the statement read.
Nato troops are scheduled to remain in Afghanistan until 2014, a position reiterated by President Obama and Prime Minister David Cameron at a meeting in Washington this week.
On Wednesday, the Pentagon reported that the soldier, who has not been named, had been flown out of the country to Kuwait.
The US Army said they had taken the soldier out of the country, as they did not have “appropriate detention facilities in Afghanistan”.
However, the move may also have been a tactic to diffuse the firestorm in Kabul following the killing, after which Afghan lawmakers had demanded that the soldier be brought to justice locally.
The massacre had placed Karzai under increased pressure to suspend talks with the US until the soldier was handed over.
On Thursday, an Afghan man who crashed a stolen vehicle on to the runway at Camp Bastion as US defence secretary Leon Panetta arrived, died of his injuries.
He succumbed to severe burns, said Lieutenant General Curtis Scaparotti, deputy commander of American forces in Afghanistan.
Wednesday’s crash at Camp Bastion is believed to be linked to an earlier incident, which left a British serviceman with minor injuries.
The driver, a local man employed at the base, was treated at the base's hospital for his injuries but died this morning.
In a statement yesterday, Nato's International Security Assistance Force (Isaf) said: "We are currently investigating to determine more facts.
"At no point was the secretary or anyone on the aircraft in any danger from this incident."
Camp Bastion was put under "lockdown" in the aftermath of the incident, with flights and movements in and out restricted while it was investigated, and Ministry of Defence police patrolled roads inside the base.