"It's been quite a week, as all of you know, and it's a week that makes us in many ways very sad," Walters said at the beginning of Tuesday's program.
"I think the Iraq war brings out a lot of very hot feelings, and we had our own hot feelings," she said.
Walters said that she and O'Donnell "have been e-mailing each other all weekend with the most affectionate notes because we are very close friends."
"And as I said last week, my admiration for her and my affection for her — Rosie, if you're watching — nothing will change that," she said.
Producers must now scramble to find fill-in hosts to replace O'Donnell, who pulled out of her contract with ABC nearly a month early following last week's dispute. On Tuesday, comedian Whoopi Goldberg substituted on the panel, and the four co-hosts discussed O'Donnell's exit briefly before moving on to other topics.
Hasselbeck said she and O'Donnell "have had incredible discussions" on the program and said they were "in communication a lot" over the weekend.
"And I think this weekend gave us the opportunity to tackle our most important hot topic yet, and that was the power of forgiveness, and I believe we've begun that process," Hasselbeck said. "And so that enables us to move on in a very positive way."
However, in a video posted Saturday on her personal blog, O'Donnell said she hadn't spoken with Hasselbeck, although she noted that the younger woman called and spoke with her partner, Kelli Carpenter O'Donnell.
"I probably won't, and I think it's just as well," she said, adding that they did exchange e-mails.
"I never tried harder to be friends with someone than I did with her, from the get-go," O'Donnell added. "But I don't think we ended up there or anywhere close which is sad."
The comedian called the bitter on-air fight "shocking" and said she was deeply upset about the producers' use of a split screen during the live clash.
"When I saw the split screen, that's when I knew it was over, seriously," she said.
O'Donnell denied reports that she and her staff trashed her dressing room before she left, but confirmed that her producer Janette Barber drew a mustache on a tacked-up magazine photo of Hasselbeck after the fight, calling it a "spur-of-the-moment" action.
The comedian said that Barber, who often appears in O'Donnell's video blogs, was "in the naughty corner."
O'Donnell seemed resolved about her decision to leave "The View," saying there was no "spirit of community" on the show.
"I was really just like the foster kid for the year," she said. "I came, we considered adoption, but I didn't really fit into the family."