According to reports, Mallika wanted to ring a bell to appreciate an act on 'The Great Indian Laughter Challenge', a practice followed by the show. Akshay had then said, "'Aap bell bajao, main aap ko bajata hun'". The colloquial word 'bajao' is believed to carry violent or sexual undertones.
Twinkle, however, argued that "bajao" was a "phrase that both men and women use" and called it a "pun on the words and actions related to ringing of the bell".
"It's a colloquial phrase that both men and women use - for instance, 'I am going to bajao him/her' or I got bajaoed', Red FM even has a tagline 'Bajate Raho' all without sexist connotations," she said.
Akshay's comment had prompted Mallika's father, journalist Vinod Dua, to slam the actor on his Facebook page. The post has since been removed by the website.
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"Mr Vinod Dua, Ms Dua's father, had written a post - it's been taken down now, stating, 'I am going to screw this cretin Akshay Kumar.' Should Mr Dua's statement also be taken literally or interpreted in context," Twinkle wrote.
"I have always stood up for freedom within comedy including defending AIB's infamous roast on numerous occasions in the past and that is my stance even today, so kindly stop tagging me in this debate," she concluded.
Akshay's comment made headlines after a video of comic Shyam Rangeela mimicking Prime Minister Narendra Modi and Congress vice-president Rahul Gandhi was leaked on social media.
Mallika, along with comedians Zakir Khan and Hussain Dalal, was reportedly fired from the show earlier this month.