In addition, CNN's New York City studio was evacuated Wednesday morning due to a suspicious package being found. In a statement, Press Secretary Sarah Sanders denounced the threatening stunts, saying "these terrorizing acts" are despicable.
The device sent to Soros was found in a mailbox outside his house on Monday and officials have said that it was likely hand delivered, according to reports in the New York Times.
The FBI said it was investigating the packages.
Earlier on Tuesday, a package containing an explosive device was found in a mailbox outside a NY home owned by billionaire financier George Soros, and the Federal Bureau of Investigation was searching for the sender.
The Secret Service said the package addressed to Clinton was recovered late Tuesday, while the package sent to the Obamas' Washington home was intercepted early Wednesday.
The devices were discovered by technicians who screen mail sent to the former U.S. officials.
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His comments prompted widespread criticism, including condemnation from CNN President Jeff Zucker, who charged the Trump administration with "a total and complete lack of understanding... about the seriousness of their continued attacks on the media".
The White House has condemned the attempted attacks.
Then on Wednesday packages addressed to Barack Obama, the former president, Eric Holder, his attorney general, John Brennan, the former Central Intelligence Agency director, and at least two Democratic Congresswomen were found.
Police in New Castle, New York - the force which covers Chappaqua - said they had assisted the FBI, Secret Service and Westchester County authorities in "the investigation of a suspicious package".
A spokesman for Mrs Clinton referred queries to the Secret Service statement.
On Thursday, without directly referencing the explosive devices, President Donald Trump again blamed the media for the "anger" in society. That's according to a person familiar with his schedule who spoke on condition of anonymity and wasn't authorized to speak publicly.