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.