Its Institute of Politics had announced on Wednesday that Manning would be one of approximately 10 visiting fellows, but the school withdrew the offer early Friday morning following controversy.
Manning is still invited to spend a day at the Kennedy School and participate in a forum with students, but Elmendorf said in a statement that designating her as visiting fellow was "a mistake."
He said the school hadn't intended to honor her or "endorse any of her words or deeds, as we do not honor or endorse any Fellow."
"I see more clearly now that many people view a Visiting Fellow title as an honorific, so we should weigh that consideration when offering invitations," he stated.
"I apologize to her and to the many concerned people from whom I have heard today for not recognizing upfront the full implications of our original invitation."
On Thursday, CIA Director Mike Pompeo canceled an appearance at a Harvard forum after taking issue with Manning's inclusion in its upcoming class of visiting fellows.
Pompeo, a graduate of Harvard Law School, said in a letter
that appearing at the event after Harvard's announcement on Manning, who was found guilty of leaking classified information, would "betray" his conscience and the trust of the people of the CIA.
"I believe it is shameful for Harvard to place its stamp of approval upon her treasonous actions," Pompeo wrote.
Manning was released from prison in May after then-President Barack Obama commuted her 35-year sentence -- a decision met with anger from those who consider her a traitor for giving information to WikiLeaks, and praise from those who argued she was persecuted for her whistleblowing.
In response to the rescinded offer, Manning tweeted that she was "honored to be 1st disinvited trans woman visiting @harvard fellow."
Former CIA Deputy Director Michael Morell likewise had taken issue publicly with Harvard's decision. He resigned as a senior fellow at Harvard University after the school's announcement.
Elmendorf's office confirmed to CNN that Morell had resigned his role. In a letter obtained by CBS News
-- Morell is a contributor for the network -- Morell said he could not be part of an organization that "honors a convicted felon and leaker of classified information."
In leaving his role with Harvard's Belfer Center for Science and International Affairs, Morell further explained in his letter that he felt he had an obligation to defend sensitive national security information and that the school's decision to appoint Manning as a fellow would "assist in her long-standing effort to legitimize the criminal path that she took to prominence."
Efforts by CNN to reach Morell were unsuccessful.
Responding to Morell's resignation, Manning tweeted "good" with the hashtag #WeGotThis.
Morell, who worked at the CIA for decades, also said that he fully supports Manning's rights as a transgender woman
and her right to serve in the military, as well as the right of Harvard's Institute of Politics to invite anyone they choose for the fellowship program. Pompeo wrote in his letter that his decision had "nothing to do" with Manning's gender identity.
Former White House press secretary Sean Spicer was also announced as a visiting fellow for the year, along with Hillary Clinton's 2016 presidential campaign manager and current CNN political commentator Robby Mook and Kansas City Mayor Sly James Jr., Harvard said in a news release Wednesday.