On Wednesday, the Liberal Democratic faction left the Duma session in protest against the outcome of the local legislature elections in the Yamal-Nenets autonomous area.
At the exit, the Liberal Democrats and other parliamentarians engaged in a scuffle.
Lyubov Sliska, the first vice speaker of the Duma, admits that disciplinary measures could be applied against Zhirinovsky.
"Men should not settle disputes in public like this. If you want to have a fight, do it between the two of you, and not in public," said Sliska.
At the same time, she believes that the reasons behind the scuffle should be clarified.
Gennady Gudkov, the leader of the People's Party, expressed regret that people would judge the work of the parliament by this incident.
Gennady Zyuganov, the Communist leader, admitted that the Communists might vote for Zhirinovsky's dismissal. "He should have long left the Duma," said Zyuganov.
Dmitry Rogozin, the Motherland leader, is also demanding Zhirinovsky's resignation.
"His behavior has compromised the entire Duma," he said at the session.
The Motherland faction plans to file a petition to the Prosecutor General's Office to open a criminal case against Zhirinovsky and to deprive him of the parliamentary immunity," said Rogozin.
Zhirinovsky, in turn, believes that the scuffle in the Duma had been provoked by Motherland parliamentarians.
"It is a provocation," Zhirinovsky told RIA Novosti. He did not comment on the Motherland's demand to dismiss him saying there was no document yet.
He cited the reason for his faction's discontent with the Yamal-Nenets election results. According to him, the Liberal Democratic Party has been under pressure in the area for nine years now, and its active members have received murder threats.
"We are beginning a lawsuit to cancel the outcome of the regional elections," said Zhirinovsky.