Karoline Leavitt, a spokeswoman for Trump's transition team, said the Trump appointees “were targeted in violent, unAmerican threats to their lives and those who live with them”.
She said "law enforcement acted quickly to ensure" the nominees' safety.
"With President Trump as our example, dangerous acts of intimidation and violence will not deter us,” she said.
Neither Leavitt nor the FBI identified any of the targets by name.
New York Republican Elise Stefanik, who Trump has named to be the US ambassador to the United Nations, was the first to say her family home had been targeted by a bomb threat.
Her office said the congresswoman was informed of the threat while she was driving with her husband and three-year-old son from Washington DC to New York for Thanksgiving.
Defence secretary nominee Pete Hegseth later confirmed that he was also targeted.
On X, he said that a police officer had shown up at his home on Wednesday morning, as his seven children were sleeping inside to notify him they had received "a credible pipe bomb threat".
"I will not be bullied or intimidated. Never," he wrote. "President Trump has called on me to serve - and that is what I intend to do.”
Trump, who survived two assassination attempts during his campaign, was not among those who received the hoax calls, law enforcement sources told US media.
He has received genuine threats recently, according to officials in Arizona who arrested a man earlier this week for posting videos on a "near-daily basis" in which he threatened to kill Trump and his family.
None of those targeted this week were protected by the US Secret Service, according to media reports.
