The 42-year-old Florida lawmaker wrote on Friday on X that “lies were weaponised to try to destroy me”.
Robert F Kennedy Jr, Trump’s nominee to serve as the head of the US Department of Health and Human Services, is meanwhile facing backlash over his vaccine scepticism.
Shares in vaccine makers and healthcare firms around the world slid sharply on Friday, as investors reacted to the nomination of a campaigner who has vowed to crack down on “Big Pharma”.
The head of the American Public Health Association, which has a 25,000-strong membership of health professionals, told the BBC that Kennedy’s criticism of immunisations had “already caused great damage in health in the country”.
George C Benjamin added that Kennedy was “just absolutely the wrong guy for it”.
Trump himself has so far not directly addressed the criticism of his picks.
The president-elect is still hiring for his incoming administration, with posts such as FBI director and treasury secretary yet to be named.