"Furthermore, the office has determined that there are no substantial reasons to believe that the opening of an investigation would not serve the interests of justice, taking into account the gravity of the crimes and the interests of victims," Bensouda said.
The statement noted that the investigation will focus on the alleged crimes committed in Afghanistan after May 1, 2003, and on other alleged crimes with clear connections to the conflict in Afghanistan that were committed on the territories of other member states after July 1, 2002.
In the case of the American targets, Bensouda said, the investigation would focus primarily on 2003 and 2004.
The ICC, established in 2002, does not have the authority to investigate crimes committed in Afghanistan before those dates, the statement said.
The court's jurisdiction is bound to investigating crimes in the territories of member states, although the UN Security Council can authorise extensions of those probes into other non-member states.
This month, Burundi - in an apparent attempt to avoid prosecution - became the first country ever to withdraw from the ICC, but the court ultimately authorised an investigation relating to alleged crimes the Government had committed anyway.
The United States is one of few nations that never formally submitted to the ICC, which was established in 2002 as the world's highest legal authority for the prosecution of war crimes and human rights abuses. But US citizens can still be charged for relevant crimes they commit in other member states.
Afghanistan has been a member state since the court's inception.
No official deadline was given for the judges to respond to Bensouda's request.