In the UK at least, under case law (Hyde v Wrench, 1840), if you give a counter offer it legally voids the original offer. So if you offer to buy something for £1m and the seller responds that they will sell it to you for £2m, the original £1m offer is legally terminated - so in the UK, legally speaking, this would count as a refusal.
Unfortunately I'm not familiar with how this translates over to US law, but I'd be interested to find out.
Unfortunately I'm not familiar with how this translates over to US law, but I'd be interested to find out.