Trump, who helped stoke Wednesday's violent riot on Capitol Hill, said earlier Friday on Twitter that he would not attend the event on Jan. 20.
"I was told on the way over here that he indicated he wasn't going to show up at the inauguration: One of the few things he and I have ever agreed on," Biden said of Trump. "It's a good thing, him not showing up."
"He's exceeded even my worst notions about him," the president-elect said. "He is one of the most incompetent presidents in the history of the United States of America."
Biden, who spoke from Wilmington, Delaware, added that he would welcome Vice President Mike Pence at the inauguration. The vice president's office did not immediately respond to CNBC's request for comment.
"I think it's important that as much as we can stick to what have been the historic precedents and circumstances of how an administration changes should be maintained" Biden said. "So if Mike — the vice president is welcome to come. I'd be honored to have him there and to move forward in the transition."
Earlier in the day, Pence spokesman Devin O'Malley said the vice president and second lady Karen Pence had not decided whether they will attend.
The vice president broke with Trump earlier in the week when he said he did not have the authority to throw out electoral ballots that certified Biden's victory. Biden said he has not spoken with Pence about the vice president's attendance at the ceremony.
Biden also offered an oblique response about his views on congressional Democrats' attempt to impeach or otherwise remove Trump from office.
"I think it's important we get on with the business with getting him out of office. The quickest way that that will happen is us being sworn in on the 20th," Biden said. "What action happens before or after that is a judgment for the Congress to make."