"There's lots of forensics on this package", he said.
The pipe bombs were packed with shards of glass and were intercepted.
The US president also returned to several of his most vitriolic attack lines against Democratic political opponents, despite the fact that the attempted mail bombs had been exclusively targeted, allegedly by an avowed Trump supporter, against leading liberal figures including several of those he demeaned.
In a statement, the Secret Service said about the incidents involving the Clintons and Obamas: "The packages were immediately identified during routine mail screening procedures as potential explosive devices and were appropriately handled as such".
Another package was sent to Time Warner's NY offices that host CNN, the channel reported.
The white house is taking the situation "very seriously". Grateful for swift response of @SecretService, @FBI & local law enforcement. He also often singles out cable news network CNN and other news media whose reporting he does not like, terming them "fake news".
"At this time the Secret Service has intercepted TWO suspicious packages - one in NY and one in D.C.", the agency said via Twitter.
The first package, which turned up on Monday, was addressed to Soros, the billionaire financier and frequent target of right-wing conspiracy theories.
The envelopes, only a few inches long, had typed letters and six stamps that bore no cancellation mark.
An earlier Federal Bureau of Investigation statement said the other packages consisted of a manila envelope with a bubble-wrap interior containing "potentially destructive devices".
A law enforcement source said the package addressed to Biden was intercepted at a DE mail facility and was similar to the others. She has called him "the poster boy for what a mob protester looks like". Most of these explosives are crude pipe bombs coming in a similar kind of yellow packages with a return address of Florida. It was compact, perhaps about the length of a wooden spoon, and contained wires and a black pipe, officials said.
Officials do not know if there are other devices out there, undelivered.
Trump has been on a rally blitz, hoping to help vulnerable Republicans ahead of the November 6 elections that will determine which party controls Congress.
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