Updated 2:45 p.m. PST with Google comment and corrects that company said on Wednesday that it would resolve the problem on Thursday.
Google says it is restoring service for a "small number" of Gmail users who have been unable to access their e-mail for the past day.
Everyone affected by the outage should have service back up on Thursday, the company said in a posting Thursday afternoon on the Google Apps discussion group.
"We know how important Gmail is to our users, so we take issues like this very seriously, and we apologize for the inconvenience," the post said.
On Wednesday afternoon, Google said in a post that the problem would be resolved by 6 p.m. Thursday.
Google will be providing a full incident report to the "very few" affected Google Apps Premier Edition customers within 48 hours of resolution, a Google spokesperson wrote in an e-mail.