I notified my current employer that I received a job offer that I intended to take but she asked for me to give her 4 days to develop a counter offer (to which I agreed). How should I respond to the company that made the offer?
Usually, offers and counter offers expire after some time (X days/weeks). Say that your current company is company A and the new company is company B, does the offer from company B expire before company A has a counter offer for you (in 4 days) ?
If no, don't do anything. Just let it rest and when you have both offers from company A and B, make your decision. Be prepared that company B may also want to counter the offer from company A. You can tell company A you need some time to think about their offer (maybe 1-2 weeks?) and use that time to negotiate a possible counter offer with company B.
If yes, you can try to get an extension on when the offer from company B expires. Do note that company B probably also knows how this game works, and this can be an indication to them that you're negotiating with other companies. They may say no to an extension, in which case you might need to try to get your offer from company A earlier.
If company A is not able to provide you with an offer before the offer of company B expires, you may be able to discuss the offer from company B with company A and gauge if company A is willing to go over it (without going into too much detail). This can give you an indication of whether or not you can wait for the offer from company A or if you can accept the offer from company B.