Trump also said that the US sanctions on Iran could last 'years' and it will deny the Iranian Supreme Leader and other officials access to financial instruments within US jurisdiction.
Quoting officials, news agency AFP reported that the US will block 'billions' more in Iranian assets and it will add Iran Foreign Minister Zarif to sanctions list 'later this week'.
Soon after Iran downed the US drone on Thursday, Trump had tweeted a warning message saying Iran had made a very big mistake.
Trump called off a planned retaliatory military strike Friday, saying the response would not have been "proportionate".
"We do not seek conflict with Iran or any other country," Trump said in a brief interaction with reporters at his Oval Office here.
"I can only tell you we cannot ever let Iran have a nuclear weapon," Trump was quoted as saying by news agency PTI.
Trump said that the executive order signed by him will impose "hard hitting" sanction on Iran and it will deny the Iranian Supreme Leader and other officials access to financial instruments
He signed the order in presence of Treasury Secretary Steven Mnuchin.
"I think a lot of restraint has been shown by us but that doesn't mean we're going to show it in the future," Trump said.
"We will continue to increase pressure on Tehran," he said.
When asked if his executive order was in response to the Iranian attack on US drone, Trump replied "you could probably add that into this" but then said, "this was something that was going to happen anyway."
"I know many Iranians living in New York, and they're fantastic people," Trump said in response to a question.
(With inputs from PTI)