Don't ask her if she needs to go: Tell Her to go use the bathroom, once every 1-2 hours; if she tries and doesn't go, send her back in after 40 minutes or so. Don't bring up the accidents.
Just curious: any big changes going on? News of a pregnancy? Sometimes regression has to do with changes in how they are playing (they get more engrossed at some periods of development), and often it has to do with the child reacting to change. Could even be within the last few day or the last couple months---some kids have a delayed reaction.
Also, keep her with you as you deal with the accidents. She cannot go play until everything is cleaned up. If she's independent enough to be going potty, she should be changing her own clothes. (if she can't do basic pull-up/pull-down pants, it might be too soon). When my son (or my preschoolers) wet, I have them go into the bathroom to change clothes, clean up, etc. and have them change themselves. I'll hold open a plastic bag for them to put their pee clothes in, or your daughter can carry her laundry to the washing machine. I don't expect kids to mop up their pee, but I do expect them to facilitate this by bringing me rags (I keep a big basket at a kid-friendly height) and packing up their plastic bags into their backpacks.
This isn't something I would punish, because you don't know why she's doing this. It sounds like most kids and regression: they are usually trying to figure something out. I believe some kids go through phases where they really try to see how long they can go before having an accident-- kind of testing their own limits. You don't say, either, what your daughter's response to these accidents are, but as a former nanny, I do know firsthand how frustrating they can be for us.
Also, if she asks for something besides underwear, be sure it's diapers, not pull-ups. They just confuse the situation.Otherwise, just be clear that "It's TIME to go to the potty" every so often (especially if your intuition is nagging at you). I even did this with 5 and 6 year olds, just made a natural space in what we were doing, so we didn't have the round and round "Do you have to go?" "No!"
Don't forget, too, that this is the age of testing autonomy, and so it's almost their job at two and three to tell you "no".
Good luck-- and wishing you much patience!
H.