“It means that if a war criminal comes here, we have jurisdiction. It wouldn’t be just US victims and perpetrators, but any war criminal who sets foot in the United States,” Mr Rosenbaum told the Guardian newspaper on Wednesday.
“I know first-hand the frustration of having war criminals here and all you can do is revoke their citizenship and deport them unless some country wants to extradite them, which in the Nazi case almost never happened.”
Mr Rosenbaum also suggested that the pursuit of those responsible for war crimes in Ukraine would be "relentless".
“So the message to perpetrators or would-be perpetrators is: if you act on criminal orders or issue criminal orders, you may well have to spend the rest of your life looking over your shoulder.
"Don’t think about being a tourist after the war in most of Europe, because if we know about you, if Ukrainians know about you, if the ICC (International Criminal Court) knows about you, you may just get arrested and extradited."
Further draft legislation could allow US courts to prosecute crimes against humanity, something every other Nato member state currently allows, excluding Italy. There are also ongoing talks about possible new laws to allow US authorities to supply evidence to the ICC in The Hague.
Mr Rosenbaum directed the Criminal Division’s Office of Special Operations (OSI) between 1994 and 2010.
Under his leadership, the Office’s work resulted in the deportations to Europe of scores of Nazi perpetrators who were subsequently found guilty of complicity in tens of thousands of Holocaust atrocities.
In 1986 Mr Rosenbaum, whose parents fled Nazi persecution in Germany, headed a World Jewish Congress probe that unveiled the Nazi past of former United Nations Secretary-General and Austria presidential candidate Kurt Waldheim.