Mittal Steel, the world's largest steel maker, said it had started talks with Arcelor, but had no plans to further increase its unsolicited offer for the Luxembourg-based rival.
Mittal's hopes of carrying out its cash-and-shares bid, worth about £15 billion, lie mainly in enough Arcelor investors rejecting an alternative deal with Russian steel firm Severstal.
"We have started discussions with Arcelor. Yesterday was the first day," Malay Mukherjee, Mittal's chief operating officer, told reporters during a trip to Almaty in Kazakhstan.
"Right from the very beginning we said we were willing to talk."
A Mittal spokesman in London added the firm had no intention of increasing its current offer, which it raised in May from an original proposal in January.
"We have no intention of raising the bid. The value of our offer is trading at a premium to the Arcelor share price."
The spokesman was responding to a report in the Financial Times newspaper which speculated that Mittal might increase its bid to around €44 a share.
Mittal's offer is worth around €34.3 a share. Asked why he believed Mittal's offer was more attractive than a deal with Severstal, Mr Mukherjee said:
"We are definitely more global, our assets are more balanced. We are in all different markets and countries. Severstal is still limited to Russia and has a very small presence in the US.
"We are convinced that our offer makes the best value for Arcelor shareholders."
Arcelor and Severstal were not available for comment.
Arcelor has launched a string of manoeuvres to escape Mittal, including extra dividends and the Severstal deal.
"It's very difficult to comment on how long a discussion will last," Mr Mukherjee said.
"The offer is very attractive even if you look at it in terms of the present stock prices," he added.
Mr Mukherjee said Mittal, which owns significant steel assets in Ukraine and Kazakhstan, was looking at ways to expand in the post-Soviet market, but did not say whether it was already in talks with anyone in the Commonwealth of Independent States.
"If you look at the CIS in totality, we are already number two. We are bigger than Severstal in the CIS," he said.
We have been leaders in consolidation. We are the ones who started this in the industry. We would like the process to continue so whatever opportunities we see, we will definitely look at them."