The president made no specific reference to the intended recipients of the packages.
Police said none of the nine devices found this week have detonated and no injuries have been reported.
Biden also owns a home in Rehoboth Beach, Delaware.
The packages addressed to Biden were intercepted at mail facilities in Delaware.
The building is located in lower Manhattan where the celebrity's company Tribeca Productions is situated.
Police removed the package sent to De Niro before sunrise, according to local media reports. It was unclear whether the package contained the same explosive device that's been sent to eight other people or media organizations in the past few days, the majority of which were recovered throughout the day Wednesday.
A bomb squad unit on Thursday morning drove in a caravan through the city after leaving the neighborhood.
"The protectees did not receive the packages nor were they at risk of receiving them", it said. "Alert authorities, call 911", de Blasio said on CNN.
Details about how authorities ultimately found the Biden package on Thursday morning in DE weren't immediately available. Debbie Wasserman Schultz, D-Fla., the former leader of the Democratic National Committee. "There's a serial bomber on the loose this morning and there could be more bombs out there".
Man arrested after 2 people are shot and killed at Jeffersontown Kroger
Eric Deacon, an emergency medical technician who was shopping at the store when gunfire broke out, said he heard a "loud bang". The suspect fled to his auto and reached Hurstbourne Parkway, but was taken in to custody nearby shortly thereafter.
Game of Chance to Pay One Winner $1.5 Billion
States receive a percentage of lottery ticket sales and then use the money to support public schools or meet other needs. The winning ticket was sold at a convenience store in the rural town of Simpsonville, with a population 22,000.
Mnuchin defends upcoming trip to Saudi Arabia in wake of Khashoggi killing
It added: "As the foreign secretary has said, this was a awful act and those responsible must be held to account". The Saudi foreign minister noted at length the strategic relationship between the USA and Saudi Arabia.
The targets of the bombs were some of the figures most frequently criticized by President Donald Trump, who still assails Clinton at rallies while supporters chant "lock her up". They also believe there is some connection between Wednesday's packages and a pipe bomb left in the mailbox of billionaire liberal donor George Soros on Monday.
"(Expletive) Trump", he said then. "It's no longer 'Down with Trump, ' it's 'fuck Trump'".
De Niro received a standing ovation at the Tony awards in NY in June for a speech attacking the president.
Two devices were sent to separate offices for Congresswoman Waters.
"This is a major concern for the Federal Bureau of Investigation, and we don't know where this person is", he explained. Debbie Wasserman Schultz in south Florida and CNN's NY offices, among others. But the packages, sent to prominent Democrats critical of President Donald Trump, heightened nationwide tensions and fears two weeks before major congressional midterm elections. A spokesman for Holder declined to comment. The package looked similar to the others and had a similar device inside, the source said.
While addressing the terror scare during a rally on the evening of October 24, Trump failed to recognize any of the victims by name, simply referring to the Democrats who received suspicious packages as "former government officials". Officials confirmed the discovery to NPR, saying the matter is under investigation. "I unequivocally condemn any and all acts of violence and terror". The post office was evacuated, and incoming mail trucks diverted. Authorities also searched an office building in San Diego that houses a newspaper before concluding there was nothing risky there.
"The president, and especially the White House press secretary, should understand their words matter".
"In these times, we have to unify", he said. "We need to come together and send one very clear unmistakable message that threats or acts of political violence of any kind have no place in America".
Police have sent the package to a secure facility in the Bronx, New York Police Department Commissioner James O'Neill said on Twitter.