Mittal Steel has no plans to improve the financial terms of its 22bn-euro (£15bn) hostile bid for Arcelor after the offer was rejected by its rival.
The Arcelor board unanimously turned down Mittal's revised takeover offer on Monday, urging shareholders to back a merger with Russian firm Severstal.
Luxembourg-based Arcelor said Mittal's offer was "inadequate" and undervalued the company.
There had been speculation Mittal may be set to up its offer a second time.
However, Mittal said it "has not made any proposal to improve the financial terms of the offer and has no intention to do so".
It continued that any indication of a willingness to improve its bid had been in terms of better corporate governance and not price.
Earlier in the day, Arcelor had said it would meet with Mittal "to review Mittal's proposals to further improve its offer".
'Attractive'
Arcelor's board unanimously rejected Mittal's approach on Monday morning.
It called the 13bn-euro plan to buy Severstal "a more attractive alternative from a strategic, financial and social point of view" and recommended that Arcelor's shareholders support the move at a general meeting scheduled for 30 June.
Should Arcelor buy Severstal - a move launched to fight the Mittal bid - it would create the world's biggest steelmaker with a turnover of 46bn euros.
Arcelor would end up with 68% of the new merged steel firm, leaving 32% in the hands of Severstal's owner, billionaire Alexey Mordashov. Mr Mordashov is said to have close ties with the Kremlin.
However, despite Arcelor's efforts to fight the Mittal deal - including paying an increased dividend - some shareholders have said they prefer Mittal to Severstal.
The European Commission has also approved Mittal's bid, clearing a regulatory hurdle which would speed up the transaction.
Rebels
Arcelor said on Monday that it would give rebel shareholders' a vote on whether to hold a special meeting on the merger with the Russian firm.
A letter claiming to represent around 30% of shareholders had been sent to the board demanding the meeting.
Mittal, the world's largest steel firm, with headquarters in the Netherlands, first launched its hostile bid for Arcelor in January, and has since then upped its offer.
It is owned by Lakshmi Mittal an Indian citizen, who lives in the United Kingdom.
On Monday, Arcelor set its share buy-back scheme price at 44 euros per share.
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