Jaya, speaking to reporters late Monday, apologised and said the comments made by her were completely unintentional and that no one should take them seriously.
She said: "I am extremely sorry if any of my comments have hurt the sentiments of the people here. It was said casually and without any prejudice.
"I have the deepest regard for the state and its language. I can even speak Marathi well and I will have respect for the state till the end of my life."
MNS chief Raj Thackeray Monday demanded an unconditional apology from Jaya for her alleged anti-Marathi utterances, failing which the party would prevent screening of all films starring any of the Bachchans in Mumbai.
He said that the actress had "insulted" the state and its people under the guise of promoting the national language.
At a film function here Saturday night, Jaya had said: "People of Maharashtra, please excuse me. I am from Uttar Pradesh so I will speak in Hindi."
However, MNS leader Shishir Shinde rejected Jaya's apology, saying that she had spoken before just a handful of journalists who did not belong to the Marathi media.
Shinde told Marathi media persons Tuesday that Jaya must call a press conference where Marathi newspapers and channels are invited and then apologise before them.
But he added that her apology would nevertheless help assuage the sentiments of all Marathi-speaking people.
After 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 tore off a huge hoarding showing Abhishek in an advertisement.
There were reports of similar acts of hooliganism from different parts of Maharashtra like Akola, Nanded and Yavatmal districts, the police said.