An editorial in the party mouthpiece Saamna slammed Shah Rukh, who made it big in Mumbai but had once said that he was a "Delhiwala".
"If that is so, then why does he not go back to Delhi?" the editorial asked.
Criticising Jaya for wanting to speak in Hindi, it expressed dismay at the manner in which people who build their careers and earn fame in Maharashtra suddenly remember their native states.
"When they come here, they are non-entities and do not even have a roof on their heads. It is the people of this state who accept them with open arms," the Saamna noted.
However, after they reach the pinnacle of professional and personal successes, these individuals suddenly seem to disown the state and its people and speak of themselves as "Biharis" and "Delhiwalas", it said.
At a film function here Saturday night, Jaya had reportedly said: "People of Maharashtra, please excuse me. I am from Uttar Pradesh so I will speak in Hindi."
The Saamna wanted to know whether Jaya would have the courage to speak Hindi or promote the language in South India or Assam, where anti-Hindi protests have often been held.
It said that in these states people are beaten for speaking in Hindi, Hindi movies are not exhibited and Hindi news not telecast on television channels.
"Unfortunately, only when the Marathi-speaking people of Maharashtra attempt to show the pride in their language and culture, fingers are pointed at them and they are taken to task," the editorial said.
Maharashtra Navnirman Sena (MNS) chief Raj Thackeray had Monday said that if Jaya had so much love for Hindi, then she and her family members could work in "advertisements and films in Uttar Pradesh".
After Raj Thackeray called for an apology from Jaya Monday, MNS activists tore off movie posters of the Bachchans outside multiplexes in suburban Kandivli, Goregaon and Dadar. MNS activists even damaged a huge hoarding showing Abhishek in an advertisement.
The party refused to accept the apology of the actress Tuesday and said Jaya must call a press conference where Marathi newspapers and channels are invited and then apologise before them.