Trump made the remarks while speaking to reporters on the sidelines of the NATO summit held in Turkey.
Trump claimed that his name is at the top of a so-called 'kill list' published by Iran.
He said, "If Iran gets the chance, they will kill me first."
Dissatisfaction with ceasefire
Trump accused Tehran of repeatedly violating ceasefire terms and said he is "not at all satisfied" with the situation.
He claimed that Iran has carried out drone and missile attacks targeting ships. He also described Iran as a 'bullying state in the Middle East' over the past few decades.
Trump said, "I do not think this deal with Iran will last long."
Warning of military action
The US President said the United States will launch more military operations against Iran if necessary.
He claimed that US forces destroyed 28 Iranian naval vessels in one night and that more vessels will be targeted if needed.
He also reiterated that under no circumstances will Iran be allowed to acquire nuclear weapons.
In Trump's words, "If Iran had nuclear weapons, they would use them."
He further said that even without a diplomatic agreement, the United States will not allow Iran to achieve the capability to build nuclear weapons.
Trump claimed that the United States could attack Iran's electricity and water supply infrastructure if necessary, although he hopes such a situation will not arise.
He also said that the United States could establish control over Iran's main oil export hub, Kharg Island, if it chooses, and retains the ability to reimpose a blockade against the country.