Khasbulatov's demand was just the latest shot in an extended duel, and may have been aimed as much at President Boris Yeltsin as at Poltoranin himself.
Poltoranin is the government's minister in charge of press and information and appears frequently to act as point man for Yeltsin.
Addressed to President Boris Yeltsin in an official letter, Khasbulatov's request came after Poltoranin accused the speaker of "undermining stability" in Russia, according to Interfax.
The letter asked the president immediately to relieve Poltoranin of his duties "for voicing insulting remarks" about him.
Poltoranin had accused Khasbulatov of sabotaging the president's efforts to achieve a working truce between government and parliament.
"The public should know that it is dangerous to deal with this man", Poltoranin told Izvestia on Friday, "We must see him as someone who would undermine stability".
Khasbulatov's office issued a statement on Saturday calling Poltoranin's remarks the "beginning of the next large-scale campaign aimed -at discrediting the activity of the Russian parliament".
That language harked back to last summer, when the speaker and president were in continual and open conflict. But after months of lambasting the government, Khasbulatov abruptly changed from antagonist to defender in parliament last month, after he and Yeltsin concluded a truce on the eve of the Supreme Soviet's autumn session.
That truce again seems to have collapsed, and Poltoranin's comments may offer the most colorful evidence of this.
Either as point man or loose cannon, Poltoranin has been particularly scathing in his public pronouncements recently. Last Friday he accused Mikhail Gorbachev of planning a Bolshevik-style coup, while he said the business activity of the Gorbachev Foundation "smells of millions".
Poltoranin's public remarks have been far in excess of the official line either of the government or the president, but how far they are sanctioned remains unclear.
Acting as an advance man for Yeltsin before the president's ill-fated trip to Japan for example, Poltoranin announced that Russia was ready to give up two of the disputed Kurile islands.
That caused a public outcry back home, forcing Russia's Foreign Ministry to announce that Poltoranin had been speaking for himself.
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