The request marks the first time that ICC Prosecutor Fatou Bensouda has targeted Americans for alleged war crimes.
Bensouda said an investigation under the auspices of the international tribunal could break through what she called "near total impunity" in Afghanistan.
The prosecutor's formal application to judges at the court also sets up a possible showdown with Washington. The United States is not a member state of the court, but its citizens can be charged with crimes committed in countries that are members.
"Our view is clear: an ICC investigation with respect to U.S personnel would be wholly unwarranted and unjustified," the State Department said. "More broadly, our overall assessment is that commencement of an ICC investigation will not serve the interests of either peace or justice in Afghanistan."
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As well as alleged crimes by American troops in Afghanistan, Bensouda wants to investigate the activities of CIA operatives in secret detention facilities in Afghanistan and in Poland, Romania and Lithuania, which also are members of the court.
Bensouda said in a summary of her request that "information available provides a reasonable basis to believe" that US military personnel and CIA operatives "committed acts of torture, cruel treatment, outrages upon personal dignity, rape and sexual violence against conflict-related detainees in Afghanistan and other locations, principally in the 2003-2004 period."
The prosecutor's office said there was reason to believe that at least 54 detainees were abused by US military personnel and at least 24 by CIA operatives.
The 16-page summary said the people likely to be targeted in any future investigations "include persons who devised, authorised or bore oversight responsibility for the implementation by members of the US armed forces and members of the CIA of the interrogation techniques that resulted in the alleged commission of crimes."
A Pentagon spokesman, Air Force Lt. Col. Mike Andrews, said the Defence Department does not accept that an ICC investigation of US personnel is warranted.