Mittleman, which holds a 17.6 percent stake in Aimia, said the offer was "blatantly inadequate" and backed the data analytics firm for rebuffing the offer and continuing negotiations.

Last week, Aimia rejected the consortium's July 25 bid of C$250 million ($192.7 million) cash and the assumption of about C$2 billion of Aeroplan points liability.

The company also rejected a raised cash offer of C$325 million and said that C$450 million would be a fair price for the loyalty program business.

"If Aimia cannot obtain at least the stand-alone value of Aeroplan, C$1 billion, plus a modest control premium of 20 percent, then I'd prefer Aimia not sell it," said Mittleman's Chief Investment Officer Christopher Mittleman, in a statement.

The Air Canada-led consortium includes Toronto-Dominion Bank, Canadian Imperial Bank of Commerce and VISA Canada Corp.

(Reporting by Anirban Paul in Bengaluru; Editing by Shailesh Kuber)