Other companies including Keurig announced they would stop advertising on Hannity's show, but later reversed course.
"For me, the judge has 24 hours", Hannity said on his Tuesday night broadcast. "We accept the apology of the Keurig CEO, and look forward to enjoying a nice cup of apolitical Joe".
FILE - In this Monday, Sept. 25, 2017, file photo, former Alabama Chief Justice and U.S. Senate candidate Roy Moore speaks at a rally, in Fairhope, Ala. "You must immediately and fully come up with a satisfactory explanation for your inconsistencies that I just showed", Hannity said, talking about Moore's hedging on Hannity's radio show Friday, and his apparent signature in the yearbook.
Two women have accused Moore of initiating sexual contact with them when they were teenagers and he was in his 30s. He is facing Democrat Doug Jones in the election scheduled for December 12.
Senate Majority Leader Mitch McConnell has called for Moore to step out of the race-but President Donald Trump is yet to comment on the matter.
Hannity did not elaborate on what would happen if Moore failed to clear up the allegations before his deadline.
Moore on Monday again denied the allegations, and in campaign events in recent days pledged to continue in the race.
In his show Tuesday, Hannity pointed to inconsistencies in Moore's account.
"Here's where I am tonight: between this interview that I did and inconsistent answers come up between him saying I never knew this girl and then that yearbook comes out", he said. "You must remove any doubt".
When asked by a Banker & Tradesman reporter on Twitter why Realtor.com deleted the tweet announcing it would pull ads from Hannity's show and how it would explain the move to its members, almost two-thirds of whom are women, a spokesperson for Realtor.com replied with a link to the company's full official statement.
The move prompted several people to destroy Keurig products in protest and post videos to social media.
"If you love the United States, if you love the Constitution and you love the American war fighter, I'm the f--ing coffee that you need to be drinking", he says.