Government officials said doing so would be a violation of free speech.
"We will not interfere with an independent television channel," one official told AFP, asking not to be named.
"The United States has a strange conception of freedom of expression. What would they say if we tried to interfere with the way Fox News portrays Arabs, Muslims or Palestinians," he said in reference to the nationalistic US network.
Hizb Allah on the other hand welcomed the US State Department's complaint against its 26-part series al-Shatat, or The Diaspora, that began airing on Monday for the Muslim fasting month of Ramadan.
"Let's face it, it's given the programme a lot of free publicity," the movement's number two, Shaikh Naim Kassim, told the rival LBC television, only half tongue-in-cheek.
He defended the programme’s content against US charges of anti-Semitism, saying it was "an artistic work based on clear historical facts."
"The United States has a strange conception of freedom of expression. What would they say if we tried to interfere with the way Fox News portrays Arabs, Muslims or Palestinians"
Un-named Lebanese official
The State Department said on Tuesday that it had complained about the series to the governments of both Lebanon and Syria on the grounds that it incorporated elements of The Protocols of the Elders of Zion, an infamous 19th-century forgery.
"We are strongly opposed to any and all displays of anti-Semitism and programming that is seen to recognise the so-called The Protocols of the Elders of Zion," its spokesman Richard Boucher told reporters.
"We view those programmes as unacceptable. Such programmes do not contribute to the climate of mutual understanding and tolerance that the Middle East so desperately needs."
The forged Protocols, which the department has called "racist" and "untrue," describes a Jewish plot for world domination and was used in Nazi Germany and other parts of Europe as a pretext to persecute Jews.
It is not the first time that the State Department has protested against Arab programming containing references to the forgery.
Last year, it objected but failed to prevent the broadcast by Egyptian television of the Ramadan mini-series Horseman without a Horse.
Washington regards Hizb Allah as a "foreign terrorist organisation" and bars its official representatives from any contact with the group.