INSURGENTS launched an attack on an Afghan Government delegation visiting the site where 16 civilians, most of whom were women and children, were killed by a US soldier.
Two of President Hamid Karzai's brothers, Shah Wali Karzai and Addul Qayum Karzai, and top security officials were part of the group travelling to the scene of the massacre in Afghanistan's Najiban and Alekozai villages when insurgents opened fire.
Police said one Afghan soldier and three militants were killed.
The Taliban has threatened to behead US soldiers in revenge for the deaths.
Taliban spokesman Zabihullah Mujahid said: "The Islamic Emirate once again warns the American animals the mujahideen will avenge them, and with the help of Allah will kill and behead your sadistic murderous soldiers."
The US soldier is accused of walking off his base in Kandahar province and gunning down the villagers.
A US official said the accused soldier had suffered a traumatic brain injury while on a previous deployment in Iraq.
The shootings, which came just weeks after deadly protests across the country over the inadvertent burning of Korans by US soldiers, triggered a protest by around 2000 students in the eastern city of Jalalabad.
The demonstrators chanted "Death to America" and demanded Afghan President Hamid Karzai reject plans to sign a pact with Washington that would allow US advisers and possibly special forces to remain in the country beyond the planned withdrawal in 2014.
US President Barack Obama, speaking after a phone call with Mr Karzai – who is said to be furious over the killings – said the shootings had only increased his determination to get troops out of Afghanistan.
However, Mr Obama cautioned there should not be a "rush to the exits" and said the withdrawal should be done in a responsible way.
Nato officials said it was too early to tell if the US soldier would be tried in the United States or Afghanistan if investigators were to find enough evidence to charge him, but he would be under US laws and procedures under an agreement between US and Afghan officials.
Typically, once the initial investigation is completed, prosecutors decide if they have enough evidence to file charges and then could move to a court martial hearing.
US Defence Secretary Leon Panetta said on Monday the death penalty could be sought in the US military justice system against the soldier, but portrayed the shooting as an isolated event that would not alter withdrawal plans.
While Afghan MPs in parliament called for a trial under Afghan law, Mr Karzai's office is understood to believe a trial in a US court would be acceptable provided the process was transparent.
Analysts said the incident would complicate US efforts to reach agreement with the Afghan Government on a post-2014 security pact before a May summit in Chicago on the future size and funding of Afghan security forces.
Nato's top commander in Afghanistan, Marine General John Allen, has promised a rapid investigation of the massacre.
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