Company asking to pay for Notice period shortfall based on India policy where I had resigned in Australia

Dear Team,
I was working in an Indian MNC who sent me onsite to Melbourne on 457 visa.
Here in Melbourne during the last few months there was no project and only expected to start which finally did not start and they planned to release me.
I had resigned from the company here at Melbourne and the Project Account where I was allocated earlier did not want to give me allocation for a single day for the month when I resigned. In these grounds the local HR of Melbourne adjusted my onshore leaves and relieved me from the company within 9 days whereas the onsite notice period is 30 days but it was purely their decision and not anything mine to release me earlier.
After that the India HR team had sent me a mail claiming a payment to be made for 81 days notice period shortfall.
I replied to that email stating that it was not my decision to get relieved earlier and the project account has made the decision so why am I liable.
Just yesterday, they had sent me a document claiming me to pay a huge amount which includes 81 days notice period shortfall amount and some others and they told that after I pay this they are going to release my relieving letter and stuff.
Could you please suggest or advise what shall I do?

Dear friend,
Even though, you were deputed on site to Australia, the terms and conditions of your employment were strictly as per the original and existing contract of employment between the Country Unit of the MNC and yourself unless otherwise specific modifications,if any, in the event of on site deputation are provided therein.

Thank you Umakanthan for the reply.
In my deputation letter that was given to me before I came to Australia, it was mentioned that we shall be following all the policies of Australia for that company.
In the India policy of separation also it is clearly mentioned that if an employee requests an early release, he/she is liable to pay the notice period shortfall.
In that case what would be your suggestion?

Sorry, I've no knowledge about temporary employment visas to work abroad. At the same time, out of common sense, I may observe that being under an employer-sponsored temporary visa and knowing well that you are likely to be released for want of work, how you took the decision to resign? Chances for the presumption are there that you might have got some other alternative employment in Australia itself. The separation conditions of the Australian Unit might be applicable to the locally recruited and appointed employees only in view of no expenses towards visa sponsorship and travel incurred by the Indian MNC. The Melbourne HR manager might have just mechanically processed your resignation and acted upon. At least you could have clarified the position with your Indian HR before tendering resignation. Negotiate with your Indian MNC for waiver of certain exit conditions as a special case.