The multinational angered workers and the government when it announced a plan in October to close two furnaces at its steel plant in Florange.
It gave the government a grace period of 60 days to look for a new owner.
The Mittal family said they were “extremely shocked” by the comments.
“We no longer want Arcelor Mittal in France because they didn’t respect France,” Arnaud Montebourg told French business daily Les Echos.
The minister, who previously opposed the closure of a Peugeot factory, accused the company of “overwhelming lies” and said the Florange closure breaks a promise made by chief executive Lakshmi Mittal during Mittal Steel’s 26.9bn-euro (£21.8bn) takeover of Arcelor in 2006, which was strongly opposed by French ministers.
The problem “isn’t the furnaces in Florange, it’s Mittal”, said Mr Montebourg.
Mr Mittal, the Indian-born chief executive, is expected to meet with President Francois Hollande on Tuesday to discuss the group’s operations in France.
The talks come ahead of a deadline on Saturday which Mr Mittal gave the state to find a buyer for the two idled blast furnaces in Florange, a traditional steel town in north-eastern France.
The government says it has received two offers, but only for the entire site. Mr Mittal has refused to sell the full operation, which employs a total of 20,000 workers.
As a result, Mr Montebourg has said he is exploring how to seize the entire Florange site should Mr Mittal refuse his demands.
According to the French newspaper, Mr Montebourg’s idea “would be a partnership with a minor manufacturer, the time to stabilise activity” in Florange.
Jean-Louis Borloo, a conservative politician and a former environment minister, also supported Mr Montebourg’s efforts.
“France’s steel industry needs to live – there are 2,200 people on the site, 22,000 Arcelor Mittal employees in France and globally, there are 75,000 [employees involved in steel],” he told France Inter radio.
The Mittal family said they were “extremely shocked” by Mr Montebourg’s attacks on the steelmaker.
One person close to the group said: “These are pretty violent comments towards a group that employs 20,000 people in France.”