"We seriously demand and expect that the government of the United States punish the culprits and try them in a public trial before the people of Afghanistan," the lower house of Parliament said in statement.
The US soldier walked off his base, heavily armed and with night vision equipment, and broke into three village homes before dawn on Sunday, killing 16 people including women and children, according to Western and Afghan sources.
Condemning the killings as "brutal and inhuman", Parliament declared that "people are running out of patience over the ignorance of foreign forces".
President Barack Obama telephoned Afghan President Hamid Karzai to promise a speedy investigation into the killings, which fanned already smoldering anger among Afghans over the burning of Qurans at a US military base last month.
Sunday's massacre poses an acute test of the US-Afghan alliance, as the two countries pursue difficult talks on securing a strategic pact to govern their partnership once foreign combat troops leave Afghanistan in 2014.
"When Afghan people are killed deliberately by US forces, this action is murder and terror and an unforgivable action," Mr Karzai said.
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