Northern Iron shares fell 3.7 percent to A$1.05 after it knocked back the bid, while the broader market was down 0.9 percent on Tuesday morning.
Aditya Birla last week proposed to offer between $1.28 and $1.35 a share, which Northern Iron said failed to reflect the improvements in quality and production rates that it expects to achieve at its iron-ore mines in Norway.
However, the NFE Board will allow access to certain limited due diligence information so that Aditya Birla Group may see fit to make a higher indicative, non-binding proposal, if it so wishes, Northern Iron said in a statement to the Australian stock exchange.
It said it had also received several other proposals not involving a full takeover, but said talks on those transactions had not gone far.
Northern Iron shares jumped last week on an Indian media report that Aditya Birla had made an offer.
Northern Iron confirmed the report last week, but said in response to a stock exchange query the report was wrong in saying Northern Iron was expecting a valuation of close to $500 million.
The top end of the proposed offer in Australian dollar terms was A$1.29, Northern Iron said, or A$477 million.