Mittal, the world's biggest steel company, launched a hostile takeover bid for its closest rival on Friday.
Mittal said the deal would create the world's first 100 million tonne-plus steel producer, with a market capitalisation of $40 billion. It anticipated annual synergies of $1 billion.
But Arcelor SA said in a statement on Sunday: "After a thorough review and analysis of the elements at its disposal, the board has swiftly concluded that Arcelor and Mittal Steel do not share the same strategic vision, business model and values.
"The board of directors has resolved that it unanimously rejects Mittal Steel's unsolicited proposal which it considers hostile."
Arcelor asked shareholders not to tender their shares in the offer, which values them at $24.50 each.
The Arcelor board said it believed that its current strategy offered the best guarantee of value creation for its shareholders.
The Mittal bid was launched shortly after Arcelor offered a significant premium to win Canadian steelmaker Dofasco Inc in a bidding war with Germany's ThyssenKrupp AG.
The Luxembourg government, the largest shareholder in Arcelor SA, voiced concerns on Sunday about the bid, citing Mittal's failure to consult Luxembourg or Arcelor's management.
Luc Frieden, Luxembourg's budget minister, and Jeannot Krecke, the economy minister, said in a joint statement that they were concerned about "the apparent hostile nature of the bid" and the lack of guarantees over employment and investment in the principality.
"The board of directors has resolved that it unanimously rejects Mittal Steel's unsolicited proposal which it considers hostile"
Arcelor SA statement
The statement said they "pointed to the lack of precise details in the bid on the future role of the Luxembourg state in the company".
Luxembourg holds 5.6% of Arcelor's shares. Arcelor is the principality's largest employer.
Lakshmi Mittal, the CEO of Mittal Steel, is due to meet Jean-Claude Juncker, Luxembourg's prime minister, on Tuesday.
The regional government in southern Belgium on Saturday called on the two companies to respect existing labour agreements with trade unions. The government said it would seek more commitments before it agreed to any sale of its 2.4% stake in Arcelor.
The company employs thousands of people in the French-speaking region of Wallonia, which has been hard hit by steel job losses in recent years.
Thierry Breton, the French finance minister, who was to meet Mittal on Monday, told France's LCI television that he "wants to know more" about the takeover bid, but said it did not favour Arcelor.
London-based Mittal heads the
world's biggest steel company
With revenue of $36 billion last year, Arcelor is the world's second biggest steel company by sales but is facing tougher conditions in its core European markets.
Rival Mittal Steel Co overtook Arcelor as the world's largest steelmaker by buying US-based International Steel Group, and trumped Arcelor to acquire Ukraine's state-owned Kryvorizhstal in a public auction last year.
Arcelor was created in 2002 through the merger of Usinor SA of France, Arbed SA of Luxembourg and Aceralia Corp Siderurgica SA of Spain.