Pershing Square Capital wants control of ADP, including five board seats and the ouster of the chief executive, two demands the payroll processing company said it has rejected.
Shares of ADP were down 0.2 percent, to $111.53, in midday trading Friday after jumping nearly 3 percent in pre-market trading.
The hedge fund run by billionaire activist investor Bill Ackman has amassed an 8 percent stake in ADP, mostly in derivatives, ADP said in a statement on Friday. Ackman first contacted ADP on August 1 asking that it extend the August 10 deadline for nomination of directors so that he can nominate five people, including himself, to ADP's 10-member board, the ADP statement said.
In addition, ADP said Ackman wanted to replace Carlos Rodriguez as CEO.
Ackman met with Rodriguez on Thursday and asked to postpone the nomination deadline but was told no, two sources told CNBC. Ackman didn't provide names of his other potential nominees, other than his own, the sources said.
CNBC's Scott Wapner interviewed Ackman later Friday morning and reports that Ackman sought a minority slate of directors and was not seeking to control the company.
In its own statement on Friday morning, ADP said, "The Board has unanimously determined that it is not in the best interests of ADP or its other shareholders to accede to Pershing Square's last-minute request for an extension." Morgan Stanley is its financial advisor and Paul, Weiss, Rifkind, Wharton & Garriso is its legal advisor.
In its statement, ADP compared it six-year stock performance under CEO Rodriguez to Pershing Square's hedge fund returns from 2012 to 2016.
"Since Carlos Rodriguez became CEO nearly six years ago, ADP's total shareholder return of 202% is well in excess of the S&P 500 TSR of 128% - and is many multiples of Pershing's TSR of 29%."
Word that Ackman was building a stake in the company sent the shares up more than 10 percent late last month. Pershing previously owned ADP shares from 2009 to 2011.