Afghan MPs were furious on Thursday as the US flew the soldier accused of slaughtering 16 civilians to Kuwait.
Relations between the US and Afghanistan had been tense even before Sunday's killings in Kandahar province, in which 16 civilians including nine children were allegedly shot and some set alight by a rogue US soldier.
Kandahar MP Mohammad Naeem Lalai Hamidzai said: "It was the demand of the families of the martyrs of this incident, the people of Kandahar and the people of Afghanistan to try him publicly in Afghanistan."
And fellow Kandahar MP Abdul Khaliq Balakarzai called on Mr Karzai to respond to the US decision to move the soldier by refusing to sign the strategic partnership agreement.
This agreement will govern the presence of US forces in Afghanistan after most combat troops leave by the end of 2014.