Hudson's Bay Company is lashing out at an American activist investor as debate rages over the retailer’s future.

HBC accused Land & Buildings of "misleading" its shareholders after the Stamford, Connecticut-based hedge fund criticized terms of the retailer's recently-announced $632-million investment by Rhone Capital in a letter released on Wednesday. 

"Land & Buildings has made allegations regarding the Rhone investment that are incorrect on their face," HBC said in its press release on Thursday.

"We urge Land & Buildings to stop misleading our shareholders. The Company is complying with all applicable regulatory requirements in respect of the transactions."

Canada's oldest retailer has been locked in a public battle with Land & Buildings recently after the activist urged HBC to consider a range of options to maximize the value of its real estate holdings, including a possible privatization and exiting Europe.

On Wednesday, HBC confirmed it had received an "incomplete, non-binding and unsolicited offer" from Austria-based Signa Holding to buy its German Kaufhof division. It also said the offer showed "no evidence of financing."

Nonetheless, Land & Buildings urged HBC to "seriously consider" the offer, adding it appeared to be "fully financed". 

On Thursday, HBC said it will abide by its fiduciary duty and review the offer, but questioned the investor's assessment of the situation.

"HBC has seen no evidence of financing of the Signa proposal. If [Land & Buildings Founder Jonathan Litt] has evidence that Signa proposal is ‘fully financed,’ he is encouraged to forward that evidence as soon as possible."