Vijayan was responding to a leave for an adjournment motion moved by opposition Congress legislator M. Vincent.
The Congress leader had pointed out media reports that Thomas, who behaves like a "crusader against corruption", has withheld crucial information while declaring his assets.
"It has now come to light that he owns 50 acres of land in Tamil Nadu since 2001," Vincent said.
He also added that Thomas is engaged with a firm that has two Israeli investors.
"He not only has withheld this information, even though the title deeds... mention Thomas as the owner, he has filed in his affidavit that this property is owned by his wife. How can he do such a thing,...," asked Vincent.
After the Vijayan government assumed office in May 2016, Thomas raided the homes of two top Indian Administrative Service officers, becoming a star.
Although Thomas has come under attack from the media following details about his land holding, he has not responded in the past three days, giving the opposition the chance to attack the Vijayan government.
But Vijayan has countered the opposition's demands for action against Thomas, and said that at the moment he does not have an answer to the land deals of Thomas.
"I will have to check... the particular land deal and related issues. Without checking on facts, I will not be able to say anything," he said.
"But one thing I can say is that for a while now there have been calls to remove Thomas and to that I wish to state, no such action is going to come...," said Vijayan.
Unhappy with the Chief Minister's statement, Leader of Opposition Ramesh Chennithala said that he too was a Home Minister and he knows the rules and regulations of the vigilance.
"Thomas has flouted the very tenets of the vigilance manual and is doing things as he pleases and is it not the reason even the court has taken the vigilance to task," Chennithala said.
"The credibility of the vigilance has eroded and you (Vijayan) and your government have miserably failed in handling the vigilance department. We never ever asked for the removal of Thomas. We only pointed out the way the vigilance is being run by Thomas," he said.
"The classic example came recently when in a crucial case involving your former cabinet colleague -- E.P.Jayarajan, the vigilance department gave one affidavit, and the government gave another one," Chennithala added.
"This clearly shows the way the affairs in the vigilance are being run," said Chennithala and expressing protest, he took the entire opposition out of the house.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)