A bench headed by Chief Justice T S Thakur said the plea is being dismissed on merit.
The bench also comprising Justices P C Ghose and U U Lalit rejected preliminary objections that the plea was not maintainable.
Justice Lalit, who pronounced the judgement on behalf of the bench, said, "We have held that the plea is maintainable.
We have dismissed the plea on merit".
Justice Katju had on June 29 last year moved the apex court seeking quashing of resolutions passed against him by both Houses of Parliament for calling Mahatama Gandhi and Subhash C Bose as British and Japanese "agents" respectively.
The former judge, in his Facebook post, had said both Houses of Parliament condemned him for his statements "calling Gandhi a British agent, and Subhas Chandra Bose a Japanese agent" without even giving him a hearing.
A former chairperson of Press Council of India, Justice Katju had sought quashing of resolutions passed against him by Lok Sabha on March 12 and Rajya Sabha on March 11.
He had also sought a direction to Lok Sabha Speaker and Chairman of Rajya Sabha that he be heard personally or through his duly designated lawyer(s).
His plea had alleged that both Houses of Parliament lacked "competence" to condemn him.
"Because, Parliament lacks the competence and authority to pass the impugned resolutions condemning the act of the petitioner, who is a private person.
"They (LS and RS) are not competent to take cognizance of expressions of free speech of a private person like petitioner as power under Rule 171 of Lok Sabha Rules provides that the resolution must relate to act of Government. Thus Impugned Resolution does not fulfill the jurisdictional requirement and necessary jurisdictional facts are lacking," it said.
The plea also referred to the reasons behind the alleged posts against Gandhi and Bose.
"That, the post in respect of Gandhiji in short made the point that by constantly using religious symbolism in politics for several decades, Gandhiji, in effect furthered the British Policy of Divide and Rule by alienating the Muslim population of the Indian sub-continent away from the national movement.
"That, the post in respect of Netaji Subhash Chandra Bose, in short made the point that through his actions knowingly or unknowingly, he ended up perpetuating Japanese imperial interest in the Indian sub-continent," the plea stated.