In an interview, Mr. Trump said he was “sick and tired of hearing from you” because he “does not have the balls to ask questions of the people that matter most.”
But the president also said he wanted to answer questions about the health care law “at the same time” as addressing a series of pressing matters, including the ongoing Russia probe and his administration’s immigration policies.
The president was scheduled to appear in the lobby of the White House on Friday afternoon, but the meeting was rescheduled for Monday, the same day the Senate votes on a repeal-and-replace bill.
Mr. Trump also is scheduled to speak at a dinner hosted by the American Enterprise Institute on Sunday, according to his schedule.
The event will be held at the White National Golf Club in Bedminster, New Jersey.
“I think this is going to be one of the most significant press conferences of my presidency,” Mr. Obama said in an interview with CNN.
“It is not something I have done in the past,” Mr the president added.
“I have done it for a few months, but I think this will be my last one.”
Mr. Obama, who spent much of his presidency under a cloud of questions about his health, took to Twitter on Friday to address the media, warning of the dangers of the media coverage of his schedule.
“What a shame it’s been the media that has been reporting on the fact that I have taken some time off to rest and recover,” Mr Trump wrote in his tweet.
“The coverage that has come out of this has been absolutely disgusting.”
Mr Trump also lashed out at the media for using a photo of him standing with a woman who was seen with a large bruise under his left eye as proof of his recovery from pneumonia, tweeting: “It is NOT true that I am ‘out of it,’ nor is it true that my doctors are saying I have a full recovery.
All these lies are the result of the fake media!”
Mr. Biden, who took the oath of office in Washington, D.C., on Friday, was in the city for a scheduled event with his wife, Jill, and other aides.
He is expected to attend a reception for former Vice President Joe Biden at the National Museum of African American History and Culture on Saturday.
In addition to the president and the vice president, there are a host of former President Bill Clinton, Vice President Al Gore and former President Jimmy Carter, along with former President Barack Obama, Mrs. Clinton and Mr. Biden.
“President Trump is taking this moment to address a very important and challenging time in the history of this nation,” said Valerie Jarrett, the former White House press secretary who is working on behalf of Mrs. Obama.
“He will take time out to answer your questions, and he is going the right way.”
“I know we have a great relationship, but there are no guarantees,” Mr Biden said on Twitter.
“When we have questions about your life, or your health, or what you are doing in this country, it is your responsibility to speak up.”
“You cannot trust the media,” Mr Clinton added.
Mr Trump has previously said he has taken the time off from his presidency to be with his family, including his sons, Eric and Donald Jr., who will begin a new chapter of their lives as president.
The White House declined to comment for this story.
Mr. Carter, the president’s former chief of staff, told The Associated Press that he and his wife “are working full time on the next phase of our lives.”
“The president has been working with the family to prepare for the transition,” Mr Carter said in a statement.
“As president, he has the opportunity to serve as the President of the United States.”
“It’s important for the president to stay with them and make sure they get the help they need to take care of themselves and their family,” he added.