The Congress members also objected to Tirumavalavan's "demeaning" remarks against their party.
"We will not tolerate any support to LTTE, which assassinated our leader Rajiv Gandhi by anybody," said Congress MLA S Jayakumar during zero hour.
Referring to the speech of Tirumavalavan, whose party is an ally of the ruling DMK, Jayakumar said the government "should not keep its eyes closed" on the activities of LTTE supporters.
Tirumavalavan had not only demanded the removal of the ban but also passed some remarks 'demeaning' the Congress, he said.
He flayed the government for permitting VCK (Dalit Panthers) to organise a public meeting recently in support of the LTTE. The Congress is an ally of the Democratic Progressive Alliance in Tamil Nadu, headed by the DMK.
Chief Minister M Karunanidhi said he did not subscribe to Tirumavalavan's views. It was a mistake on his part to criticise the Congress and the AIADMK Supremo Jayalalithaa, he said.
Quoting a recent Supreme Court judgement on a POTA case, he said the Apex Court had stated that seeking support of a banned outfit was not a crime.
This triggered protests from Congressmen, who walked out of the house.
As Congress members continued to protest, Karunanidhi assured them that all legal steps would be taken to prevent LTTE's supporters activities.
He said he was even prepared to enact a law with legal experts to stop the activities of LTTE supporters.
"We have to deal with supporters of LTTE legally. The Supreme Court, in its verdict on a POTA case, has stated that speaking in support of banned organisation is not a crime. But do not think that I am subscribing to Tirumavalavan's remarks by this" the chief minister said.
However, his explanation did not satisfy Congress MLAs, who staged a walk out. Earlier, AIADMK MLAs staged a walkout even as Karunanidhi was replying to the points raised.
"It is better for the leaders to refrain from speaking on matters, which will disturb public peace. It is good for themselves and for the government," he said.
Karunanidhi said his stand on LTTE should be seen in two parts - one before former prime minister Rajiv Gandhi's assassination and another after 1991. "Nobody can forget Rajiv Gandhi's assassination. At a young age, he had become a saga," he said.
He said Congress leaders were feeling hurt over remarks of some persons last week and had been expressing displeasure for the happenings during this period.
Even in the DPA, there were two factions - one supporting the LTTE and another against it, he said.