In a statement, the Secret Service said that the package addressed to Obama was intercepted by agency personnel in Washington, D.C. on Wednesday morning. In a statement, Press Secretary Sarah Sanders denounced the threatening stunts, saying "these terrorizing acts" are despicable.
Also Wednesday, a police bomb squad was sent to CNN's offices in New York City and the newsroom was evacuated because of a suspicious package.
Barack Obama and Hillary Clinton were mailed pipe bombs.
A bomb squad removed another device from CNN's NY headquarters, which was evacuated.
A package addressed to Bill and Hillary Clinton's home in Chappaqua, N.Y., was recovered late Tuesday, the Secret Service said in a statement to Yahoo News.
Meanwhile, a suspicious package was also sent to Democratic Party Representative Maxine Waters, AP reported.More news: Federer not disappointed post final defeat
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"ALERT! We are working an investigation of a suspicious package near Sawgrass Corporate Parkway".
However, it is not immediately clear where the explosive device was sent, whether to residential or office buildings.
CNN evacuated its offices in the building as a precaution after the discovery of the package.
The NYPD say they can not confirm whether the suspect package is the same as those found in the Clinton and Obama case.
According to a report by The New York Times, two explosive devices were discovered during routine mail screenings conducted by the politicians' staff.
President Donald Trump has termed as abhorrent the sending of suspicious packages to Mr Obama, Ms Clinton and CNN.
Earlier in the week, a suspicious package was found in philanthropist George Soros's house in NY.
So far, no one has claimed responsibility for either attack.