Several of the people President-elect Donald J. Trump has picked to be cabinet nominees or for White House positions received threats on Tuesday night and Wednesday morning, a transition spokeswoman said.

The spokeswoman, Karoline Leavitt, said several cabinet nominees and others were targeted with “violent, un-American threats to their lives and those who live with them.” Law enforcement and other authorities “acted quickly to ensure the safety of those who were targeted,” she added.

The F.B.I. said in a statement it was aware of the bomb threats and so-called swatting calls, which entail contacting law enforcement to falsely claim a dangerous person is at a particular address. Such calls are designed to create a frantic armed police response to frighten, harass and endanger someone at their home.

Three people familiar with the threats, speaking on condition of anonymity to discuss an ongoing investigation, said one of those targeted was Susie Wiles, Mr. Trump’s campaign manager whom he has tapped to serve as the White House chief of staff.

Representative Elise Stefanik of New York, Trump’s pick to be ambassador to the United Nations, was notified by the police that a bomb threat had been made against her home in Saratoga County, according to a statement from her office. She and her family were not there at the time.

Lee Zeldin, a former congressman from Long Island who is Trump’s pick to lead the Environmental Protection Agency, said the police had contacted him about a pipe bomb threat made to his home. The Zeldin family was not there at the time, he said in a statement.

Brooke Rollins, whom Mr. Trump said he would nominate to be agriculture secretary, wrote on social media that she had also been targeted and thanked the police in Fort Worth, Texas, for their response.

Howard Lutnick, Mr. Trump’s pick for commerce secretary, also received threats at his home on the Upper East Side of Manhattan on Wednesday, according to two people with knowledge of the incident. The New York Police Department said it had responded to “terroristic threats” there and had made no arrests.

Bomb threats and swatting calls are a growing problem for American law enforcement, as it has become easier to anonymously contact the authorities or leave threatening messages. Prominent public officials, schools and celebrities are often victims.