Donald Trump’s third national security adviser, John Bolton, did not brief the president on suspicions Russia might be behind mysterious “Havana syndrome” attacks on US diplomats because he did not think Trump would support him.

“Since our concern was that one of the perpetrators – maybe the perpetrator – was Russia,” Bolton said, “we didn’t feel we would get support from President Trump if we said, ‘We think the Russians are coming after American personnel.’”

Bolton makes the startling admission in an interview for an episode of a podcast, The Sound: Mystery of Havana Syndrome, hosted by the former Guardian journalist Nicky Woolf and released on Monday.

Bolton was national security adviser from April 2018 to September 2019, a period of intense scrutiny on Trump’s relations with Russia, primarily via special counsel Robert Mueller’s investigation of Russian election interference and links between Trump and Moscow.

Mueller issued his report in April 2019. He did not prove collusion between Trump and Moscow in his 2016 election victory over Hillary Clinton but the former FBI director did secure indictments of figures close to Trump and lay out extensive evidence of possible obstruction of justice.

Trump angrily rejected allegations of wrongdoing and claimed to be the victim of a witch-hunt. But he also closely courted Vladimir Putin, even seeming, in Helsinki in July 2018, to side with the Russian president against his own intelligence agencies.

“Havana syndrome” refers to the investigation of more than 1,000 “anomalous health incidents” involving diplomats, spies and other US government employees around the world. The first cases emerged in 2016.

Symptoms have included brain injuries, hearing loss, vertigo and unusual auditory sensations. Speculation about directed energy weapons has persisted, though earlier this month an official report said “available intelligence consistently points against the involvement of US adversaries in causing the reported incidents”.

Havana syndrome got its name because, as Bolton told The Sound, “the first reports came from Cuba [so] it would not be unreasonable to say the Cubans were doing it”.

But, he said, “it becomes counterintuitive pretty quickly. If they wanted to keep the American embassy open, you wouldn’t attack it. That tended to show that it was some other government. And a government with more capabilities than we thought the Cubans had.”

The Trump administration cracked down on Cuba anyway, returning it to the “state sponsor of terror” list, ending a diplomatic thaw begun by Barack Obama. Bolton, a famous rightwing foreign policy hawk, told The Sound he favoured taking that step anyway, regardless of the origin of the Havana syndrome attacks.

He also said he and other national security staffers “felt that because it was possible – not certain, but possible – this emanated from a hostile foreign power and we had our ideas who that might be … we thought more needed to be done to consider that possibility and either find evidence to rule it in or rule it out”.

If the attack theory was real, Bolton said, there was “no shortage of evidence that would point to Russia as … at least the top suspect”.

Nonetheless, he said, he decided not to take that suspicion to Trump.

“Who knows what he would’ve said,” Bolton said of his decision not to brief Trump on his suspicions about Russia and Havana syndrome.

“He might’ve said, ‘Do nothing at all.’ I didn’t want to chance that, because I did feel it was serious.”

Trump fired Bolton in September 2019. The following year, Bolton released a book, The Room Where It Happened, in which he was highly critical of his former boss. Trump sought to prevent publication. Bolton has said he could run for the Republican presidential nomination in 2024 if it is a way to stop Trump, who he has called “poison” to the Republican party.

Speaking to The Sound, Bolton suggested the decision not to brief Trump about suspicions about Russia damaged attempts to investigate the Havana syndrome mystery.

“When you don’t have the ability to bring the hammer down and say, ‘Find the answer out,’ … it’s much easier for the bureaucracy to resist.”