He, however, lost his composure as the questions increased.
"The media need not question me like the way police questions," a peeved Balakrishnan said.
"Binoy is an adult and he has his own family and now with the allegations coming out, it's his responsibility to prove his innocence. If a member of a party member does anything, it does not become the responsibility of the party. Neither me nor the party will do anything in this case to help him," he said.
In the FIR filed at the Oshiwara police station in Mumbai's Andheri area, a 33-year-old Mumbai-based woman, who hails from Bihar, has alleged that Binoy Kodiyeri sexually exploited her for several years on the promise of marriage and claims they also have a child.
According to her complaint, she entered into a relationship with him while working at a dance bar in Dubai in 2008 and now has an eight-year-old child with him. She alleged that till 2015, he even used to send her money every month.
The victim has also handed over some crucial documents, including pictures, to the police.
In reply to a question if he saw his son recently, Balakrishnan said that he has not seen him after the police started looking for him, and asked him if he will go out to find him and hand over to police, he retorted: "I am not part of the Mumbai police and it's not my job."
When a reporter mentioned how his sons are often in trouble like "being caught in the midst of a financial fraud", the CPI-M leader said: "Is it possible for me to go after them all the time and look up what they are doing. If so, then all this would not have happened. This should be a lesson for parents."
As a reporter said that the victim has alleged that Balakrishnan's wife had met her to resolve the issue, he said that he could not comment since the issue is now sub-judice. "I know you are provoking me, so I make a comment and then I also face legal issues," he said.
He dismissed media reports on Saturday morning - before crucial party committee meetings began - that he has offered to quit. "Nothing of that sort has happened and it's nothing but a media creation," Balakrishnan said.
He also said that if there is any wrong-doing on his part, his party will take appropriate action.
"Even our party General Secretary has made it clear that this is got nothing to do with our party and it's not a party issue also," said Balakrishnan.
A court in Mumbai is to rule on Binoy Kodiyeri's anticipatory bail plea on Monday.
( With inputs from IANS )