A promised feature obliging members to reset passwords when they next logged in has not yet been made available.
Instead the auction site has added a notice to its homepage, simply recommending users update passwords "as a first step".
Security experts said its reaction raised "serious questions".
"We know that customers are concerned, and want us to fix this issue straight away, and we are working hard to do just that," eBay told the BBC.
"Our first priority is and always has been to protect our users' information and ensure we correctly deal with the technical challenges such a situation brings, and that is why as a first step we have requested all users change their passwords.
"Other steps, including email notification, will follow, and we will ensure all eBay users have changed their passwords over the coming days."
Many of its users were angry about how slowly the firm had dealt with the problem.
"Just wondering why I'm hearing this from BBC before eBay," said one reader of the BBC website.