Western Resources said it planned to arrange an emergency shareholders' meeting to unseat Mr Ashcroft and the ADT board.
Only three months ago ADT eluded a $5bn bid by another US security firm, Republic Industries. Republic was forced to withdraw after the value of its stock unexpectedly tumbled.
There was no immediate reaction from Mr Ashcroft or ADT. Stock in ADT soared 16 per cent in early New York trading, reaching $23.375 a share. Tuesday's closing price was $20.125. The offer prices ADT shares at $22.50 each, which would value the entire company at $3.5bn. Western Resources is already the owner of 27 per cent of ADT stock.
Already this week, Western Resources agreed to buy the home alarm unit of Westinghouse Electric for $368m.