Cuomo, a prominent Democrat and Trump critic, is currently running for reelection. A NYPD spokesman said later in the day that the package sent to Cuomo was not a bomb, and was unrelated to the other devices, according to the Associated Press.
In a statement, Cuomo spokesman Rich Azzopardi said that a "preliminary investigation on the package at Governor Cuomo's office shows it is computer files on the hate group, The Proud Boys, who recently appeared in New York."
Clinton spokesman Nick Merrill said in a tweet that "nothing" sent to Clinton "got to any home."
The Secret Service said the package addressed to Obama was intercepted by agency personnel in Washington on Wednesday morning.
"The packages were immediately identified during routine mail screening procedures as potential explosive devices and were appropriately handled as such. Both packages were intercepted prior to being delivered to their intended location. The protectees did not receive the packages nor were they at risk of receiving them," the agency said.
A short time later, NBC reported that New York police had been called to the Time Warner Center in midtown Manhattan to investigate another suspicious package.
The headquarters of CNN, which is frequently criticized by Trump, are located in the Time Warner Center. In a memo sent to CNN employees, the news outlet's president, Jeff Zucker, said to "remain calm and patient."
CNN reported that the package found at the Time Warner Center was addressed to former CIA Director John Brennan in care of CNN. Brennan, who served during the Obama administration, has become a virulent critic of Trump and has excoriated the president on television as a contributor to MSNBC, a sister news network to CNBC. Trump stripped him of his federal security clearance in August.
The Secret Service said that reports of a suspicious package addressed to the White House are "incorrect."
Later on Wednesday, Harris spokeswoman Lily Adams said in a tweet that the San Diego Police Department was investigating "suspicious packages" that led to an evacuation of the senator's office.
NBC, citing local police, reported that an item in question was not addressed to Harris or her office, and was determined not to be a device of any kind.
Wasserman Schultz was the former chairwoman of the Democratic National Committee before running for Congress. She resigned that DNC position after her e-mails were hacked during the 2016 presidential campaign.
"I have been in direct contact with the FBI and other law enforcement officials who are working tirelessly on this investigation, and I am grateful for their efforts to keep us safe," Wasserman Schultz said in a statement Wednesday afternoon.
"We will not be intimidated by this attempted act of violence. This appalling attack on our democracy must be vigorously prosecuted, and I am deeply disturbed by the way my name was used. Today, my staff and I will hug each other and our loved ones tightly, and tomorrow get back to work serving the people I was elected to represent," Wasserman Schultz added.
Waters, an especially vocal critic of Trump who has repeatedly called for his impeachment, said in her own statement: "I have been informed by U.S. Capitol Police that my Washington, DC office was the target of a suspicious package that has been referred to the FBI."
"I am appreciative of the law enforcement entities who intercepted the package and are investigating this matter. I unequivocally condemn any and all acts of violence and terror," Waters said.
New Castle Police Lt. James Carroll told CNBC his department has assisted the FBI and U.S. Secret Service in investigating the package sent to the nearby home of the Clintons. It was discovered Tuesday night.
In a tweet Wednesday morning, the New York branch of the FBI acknowledged the existence of the package sent to the Clintons, but said it would decline further comment on the ongoing investigation.
A spokeswoman for Obama declined to comment and referred CNBC to the Secret Service. Clinton representatives did not immediately respond to CNBC's requests for further comment.
Hillary Clinton is currently in Florida to attend a fundraising event, NBC reported. Bill Clinton was at the New York home.
Senior Republican lawmakers were quick to condemn the actions against their political opponents.
contributed to this report.