A Belgian lawyer says he is preparing a case that could see General Franks charged under a law which allows the prosecution of non-Belgian citizens for war crimes.
The most famous such case was brought against the Israeli Prime Minister, Ariel Sharon, and caused deep strains in the relationship between Belgium and Israel.
If this prosecution goes ahead, Bush administration officials are making it plain they will regard it as a major diplomatic incident - an example of political harassment.
A senior administration official warned that even the issuing of indictments would result in what he called "diplomatic consequences" for Belgium.
The State Department spokesman, Richard Boucher, said the Belgian authorities should act early to prevent such consequences.
"We believe the Belgian Government needs to be diligent in taking steps to prevent abuse of the legal system for political ends," he said.
The row erupted after a Brussels lawyer gave an interview to American newspapers in which he said he was aiming to file a case next week on behalf of 10 Iraqi civilians alleging among other things that General Franks did nothing to stop the looting of hospitals in Baghdad and that coalition forces fired on an ambulance.