Ackerman is playing fast and loose with the facts and hurting the company, Engibous shot back.
The publicly released letter and response came a day after Ackman demanded in another letter Penney's board replace Chief Executive Officer Mike Ullman by next month.
The struggling midrange department store chain brought Ullman back as interim CEO in April after former Apple Inc. executive Ron Johnson was ousted as CEO after 17 months.
Ackman had supported Johnson, "under whose leadership performance deteriorated precipitously," Engibous said in a statement Thursday in response to Ackman's first letter.
After the second letter, Engibous labeled Ackman's statements "misleading, inaccurate and counterproductive."
He used "counterproductive" Thursday too in describing Ackman's first letter, which he also said was "disruptive ... at an important stage in the company's recovery."
Engibous said Thursday the board backed Ullman with "overwhelming support," saying Ullman had "led significant actions to correct the errors of previous management."
Still, the company began a CEO search "in earnest three weeks ago" and intended to conduct a "careful and deliberate" process, he said.
On Friday, he said the board was "following proper governance procedures" and said board members were "fully informed" and were "making decisions as a group," despite Ackman's allegations to the contrary.
"This includes the CEO search process, which is being conducted at an appropriate pace," Engibous said.
Ackman -- a billionaire hedge-fund manager whose Pershing Square Capital Management LP is Penney's largest shareholder -- wrote earlier Friday he had "lost confidence in our chairman's ability to oversee this board."
He said he "would therefore recommend that Tom be replaced as our chairman."
Ackman -- who launched activist campaigns against McDonald's Corp. and Wendy's Co last decade -- said in his letter Engibous showed favoritism and didn't always do what was best for the 111-year-old chain.
"The board must be led by a chairman who is unbiased, can make decisions without regard to personal relationships, and focused only on what is best for the corporation," Ackman said.
"We are now flying blind," he said.
The letter alleged the board had become impotent, he was excluded from knowing about major personnel decisions and vital financial information was being withheld from him and his Pershing Square analyst team.
On the last point, Ackman said his team was "cut off from access to information ... despite the fact that when I joined the board, the company explicitly agreed in writing to allow the Pershing Square analysts access to information so that they could assist me in analyzing the financial affairs of the company," The Dallas Morning News and other news outlets reported.
Ackman accused "a small subset of the board" of "negotiating and speaking on behalf of the full board."
He said Penney's "very existence" was at risk and during the current "very critical stage in its history ... it is absolutely critical that we work together to solve our problems."
"It is essential that our board function extremely effectively or we will certainly fail," he said.
Ackman told CNBC last year he also hoped to take an activist role in Procter & Gamble Co.