A ministry statement issued today says the demand was expressed orally to the U.S. Embassy in Bishkek.
President Kurmanbek Bakiev has vowed personally to oversee a Kyrgyz criminal investigation into the shooting.
State Secretary Adakhan Madumarov announced the Kyrgyz president's personal involvement in the probe after Bakiev met with U.S. Ambassador Marie Yovanovitch and the commander of the U.S. military base at Manas Airport, where the incident occurred.
Manas is the only U.S. base in any of the five Central Asian republics, and serves as a key facility to support operations in nearby Afghanistan.
The base leadership said in a statement posted on its website that the soldier who shot the Kyrgyz man acted in self-defense and that the incident was under investigation. It gave no further details.
U.S. Ambassador Yovanovitch reportedly told Bakiev that the soldier would be tried by a U.S. military court if investigators concluded that he had acted improperly.
Bakiev's office, in a statement earlier today, demanded that the soldier not leave the country while the investigation was under way. He also demanded that the Kyrgyz Foreign Ministry investigate the legal status of U.S. troops garrisoned at Manas.
The Foreign Ministry reiterated that Kyrgyz officials want the soldier, identified as Zachary Hatfield, to remain in the country.
The presidential statement quoted Bakiev as saying it would be "more appropriate" if U.S. soldiers answered for "illicit actions" in Kyrgyz courts.
Kyrgyzstan granted immunity from local prosecution to American soldiers in a deal that was struck early on in the U.S. military's use of the Manas facilities.
The circumstances of the shooting are unclear. The victim, whose name was given as Aleksandr Ivanov, was driving a fuel truck and reportedly requested permission to enter the base.
Kyrgyz media say the U.S. soldier shot him twice in the chest.
Kyrgyz State Secretary Madumarov said today that the incident "doesn't do credit" to the U.S. military.
Base Used Since 2001
The U.S. Air Force has been renting the Manas air base from the Kyrgyz government since 2001, when operations began to oust Al-Qaeda and Taliban elements from Afghanistan after the September 11 terrorist attacks against the United States.
The Kyrgyz government recently demanded, and got, a renegotiation of the lease terms for the Manas facilities. Kyrgyz critics of the arrangement have complained of noise and the environmental effects of the U.S. presence.
NATO also commands more than 32,000 troops from more than 30 countries under its International Security Assistance Force (ISAF) in Afghanistan.
(president.kg, manas.afnews.af.mil, Kabar, 24.kg, AKIpress)