The company also noted those who have already tendered shares can withdraw them by 12:01 am EDT on October 4 by following instruction in the TRC offer documents.

The offer comes at a time when rival Automatic Data Processing has been facing a proxy fight from investor Bill Ackman, whose Pershing Square Capital Management had been seeking control of the that company.

TRC says the move is only for investment purposes and it has no intent to influence the board of directors or management. In its SEC filing, Paychex wrote, "Nonetheless, Paychex does not endorse this unsolicited mini-tender offer and recommends that shareholders do not tender their shares in response to the offer."

Paychex says the purchase pricing is 4.07 percent lower than the closing price of Paychex shares on September 1, the last trading day before the mini-tender offer began. It also said the offer "is subject to a number of conditions."