The push for board seats comes as the Bloomingdale's parent struggles with weak demand as customer cut back spending due to elevated inflation and high borrowing costs.
But the company beat market expectations for quarterly results in November on efforts to trim inventory and strong demand for its beauty products.
"Arkhouse and Brigade have yet to provide any financing details ... of their proposal despite multiple opportunities to do so and instead ... Arkhouse has chosen to launch a proxy contest," Macy's said.
Arkhouse and Brigade Capital did not immediately respond to Reuters queries on their latest move and on how much stake they own in Macy's.
The company, famous for its annual Thanksgiving Day parade, said it would evaluate Arkhouse's director candidate and that it was committed to "long-term value creation".
Shares of the New York-based company, which is yet to decide on a date for its 2024 annual meeting, were down 0.3% in premarket trading.
