Clinton had been scheduled to appear with Obama in Wisconsin on Wednesday, after he endorsed her as the Democratic candidate for November's presidential election, but this has been pushed back, her campaign said.
The White House also confirmed the delay, announcing: "In light of the attack in Orlando, the President's travel to Green Bay, Wisconsin scheduled for Wednesday has been postponed."
Earlier, Obama had made a brief televised address to confirm that the attack on a gay nightclub in Orlando,
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The suspected gunman, 29-year-old Omar Mateen, had previously been probed by the FBI for alleged links to Islamist radicals but was not under surveillance and had a gun permit.