"I had a conversation with Bill right before we, I guess, agreed to disagree that he was going to launch a proxy contest, and I asked him, 'Bill, I know you have a vacation, which is what's getting in the way and why you need to have an extension of this deadline, but when you get back from vacation, why can't we meet then?" Rodriguez told "Mad Money" host Jim Cramer on Monday.
Earlier Monday, ADP announced that its board unanimously rejected Pershing Square's three board nominees, including Ackman.
According to Rodriguez, Ackman responded to the meeting request by saying he was not ready with his presentation. It eventually came out as a 167 slide show on ADP's alleged pitfalls.
Rodriguez said he and his management team saw Ackman's presentation when it was released to the public, and that he would have appreciated the chance to meet with Ackman before its release to correct some of the report's "wrong conclusions."
"I said, 'Well, when you're ready, we'll meet, whether it's late August, September,'" Rodriguez continued about his call with Ackman. "And he said, 'I'm afraid that's not going to work because that's not the way my business works. I have to have the leverage over the threat of launching a proxy contest in order to get you guys to agree to the things that I want to do with the company.'"
In response to CNBC's request for comment, Pershing Square labeled the above correspondence as "totally false."
The presentation called into question ADP's sales results and number of clients among other points that served Ackman's argument that the company is undervalued.
"We kind of take offense to the implication that we are, I guess, playing with numbers or not disclosing information that we should be disclosing," Rodriguez said.
For one, Rodriguez said the report used data from a 2009 presentation that included certain standalone clients — ones for whom the human capital management company only does one part of its services, like tax filing — which made ADP's number of clients look like it had decreased since then when it had not.
Rodriguez also challenged the allegations that marked his company as unproductive, saying ADP had far outpaced the S&P 500 index and Ackman's own fund in terms of performance.
"[ADP's stock is] up 200 percent, S&P is somewhere around 80 to 90 percent over the same period," Rodriguez told Cramer. "And, if I can add, because I think it's public information, Pershing Square is up ... 22 percent before fees and 7 percent after fees. Now, I'm not sure how it's possible to have that much in fees to have your return go down by that much, but that's what the published letter is from Pershing Square."
On Monday, ADP said none of Pershing's board nominees would bring "additive skills or experience to ADP's board."
Whether or not the proxy fight continues, Rodriguez said he hopes Ackman would convert his stock ownership into a true position rather than leveraging it on stock options.
Rodriguez also said he and his colleagues didn't take the fight personally.
"Despite what you might think, we're professionals and we don't take things personally," he told Cramer. "So I think the manner is less important than the facts. And I think the facts speak for themselves. The performance that we have versus Pershing Square, the ideas which have been brought up which are not new to us and not new to the board of directors or to the management team. So I think it's a deeper issue than the manner and the form in which it was presented, but it was an odd way to approach a company."