The Pentagon spokesman, Mr Ken Bacon, said yesterday the murder of Brig Saunders "highlights again that Greece needs to take a tougher stance towards terrorism".
Concern about a lax attitude towards terrorism on the part of Greece had already been expressed twice this year in Washington.
Last week a report by the National Commission on Terrorism recommended to President Clinton that Greece and Pakistan be designated as countries "not co-operating fully" against terrorism.
This would be a less severe sanction than being listed as a "state sponsor" of terrorism, under which heading the State Department lists seven countries. But the "not co-operating fully" listing would bar Greece from buying US military equipment.
The commission also recommended that nations in this category be removed from the "visawaiver" programme, which allows citizens of friendly countries such as Ireland to travel to the US without visas.
The commission said Greece, a NATO ally, "has been disturbingly passive in response to terrorist activities". The report said: "Since 1975 there have been 146 terrorist attacks against American interests in Greece. Only one case has been solved and there is no indication of any meaningful investigation into the remaining cases."
Since 1975 four US officials have been killed in Greece, but no arrests have been made.
The Secretary of State, Ms Madeleine Albright, dismissed the call for sanctions against Greece, saying she and President Clinton had raised the issue of terrorism with Greek leaders in private.
But her own department's annual report on terrorism earlier this year was also critical, describing Greece as "one of the weakest links in Europe". Greece ranked second in the world after Colombia for the number of anti-American terrorist attacks.
The report said: "The absence of strong public government leadership contributed to the lack of breakthroughs against terrorists" in Greece. "Popular opinion-makers downplayed terrorism as a threat to public order."
The November 17 terrorist group first made its appearance with the murder in 1975 of Richard Welch, head of the CIA station in Athens.