WASHINGTON — Former Secretary of State Colin L. Powell, who served as President George W. Bush’s top diplomat, derided Donald J. Trump as a “national disgrace” and an “international pariah” in personal email exchanges that were leaked online Tuesday.

In the emails, reported by BuzzFeed News, Mr. Powell also accuses Mr. Trump, the Republican nominee for president, of having embraced what Mr. Powell called a “racist” movement when he questioned the validity of President Obama’s birth certificate.

An aide to Mr. Powell confirmed the hack and said, “They are his emails.”

“Yup, the whole birther movement was racist,” Mr. Powell wrote in an email to a former aide, according to BuzzFeed. “That’s what the 99% believe. When Trump couldn’t keep that up he said he also wanted to see if the certificate noted that he was a Muslim. As I have said before, ‘What if he was?’ Muslims are born as Americans everyday.”

Mr. Powell’s emails appeared online at a website called DCLeaks.com, according to BuzzFeed. The site has previously posted documents from hacking into prominent Democrats and some Republicans, according to news reports. In July, The Intercept reported on emails leaked to the site from Gen. Philip M. Breedlove, the former commander of NATO forces in Europe.

An aide to Mr. Powell, a retired general who also served as the chairman of the Joint Chiefs of Staff, responded Wednesday morning to an inquiry about the emails: “We are confirming that General Powell has been hacked and that they are his emails. We have no further comment at this time.” Mr. Powell did not respond to an email sent directly to his personal account.

In a separate leaked email exchange reported by NBC News, Mr. Powell also criticized aides to Hillary Clinton, the Democratic candidate for president, for their attempts to “drag me in” to the controversies surrounding her use of a private email server when she was secretary of state.

In that email, Mr. Powell lamented that he had repeatedly told Mrs. Clinton’s “minions” that they are “making a mistake trying to drag me in, yet they still try.”

In her interview with the F.B.I. into the use of the email server, Mrs. Clinton told investigators that Mr. Powell had advised her to use a personal email account, according to notes of the interview disclosed to members of Congress by the bureau last month.

The Associated Press reported that in another leaked email, Mr. Powell, using Mrs. Clinton’s initials, wrote that “Everything HRC touches she kind of screws up with hubris.”