Iran has insisted its nuclear programme is entirely peaceful and denied that it is seeking to develop nuclear weapons.
However, Trump said in the NBC interview that Iran was “going to have a nuclear weapon within one month” before he ordered US air and missile strikes on three key Iranian nuclear facilities during a 12-day war between Israel and Iran last June.
The Israeli military also targeted Iran’s nuclear facilities and nuclear scientists during the war, as well as its military commanders and missile arsenal.
Trump said the strikes “obliterated” Iran’s uranium enrichment capacity, but that Iranian officials “were thinking about starting a new site in a different part of the country”.
“We found out about it. I said, ‘You do that, we’re going to do… very bad things to you.'”
Trump also told Iranian protesters that “we’ve had their back”, following the brutal crackdown by Iranian security forces on the anti-government unrest last month.
The protests were sparked by anger over the collapse of the Iranian currency and soaring cost of living, but they quickly widened into demands for political change.
The full scale of the bloodshed resulting from the crackdown is still not known because of an internet shutdown imposed by the government since it escalated on 8 January.
However, the US-based Human Rights Activists News Agency (HRANA) has said it has confirmed the killing of 6,445 protesters, 164 children, 214 people associated with the government, and 60 bystanders. It is also investigating reports of another 11,280 deaths.
Iranian authorities have acknowledged that at least 3,117 people were killed, but said the majority were members of the security forces or bystanders killed by “rioters”.
Khamenei described the unrest as “sedition” orchestrated by the US and Israel.