Bolton did not rule out sanctions on European countries that do business with Iran.
Secretary of State Mike Pompeo said Sunday that withdrawing from the 2015 agreement wasn't aimed at Europeans, but he didn't rule out the US imposing sanctions on entities that continue to do business with Iran, even as efforts continue to strike a new deal.
"There's a lot we can do to, and we should do it", said Bolton, who at the time was with the American Enterprise Institute think tank.
Protesters in Tehran and other cities carried posters which read, "Mr. Trump, you are talking nonsense", as they echoed Iranian Supreme Leader Ali Khamenei, who on Wednesday accused the USA president of telling lies about the deal and calling his decision to withdraw from the agreement both "silly" and "impudent".
If the deal collapses completely, global monitoring of Iran's nuclear facilities and restrictions placed on the country's nuclear program could end, while sanctions demanded by the US on the Iranian oil industry and other sectors could be reimposed.
"I'm hopeful in the days and weeks ahead we can come up with a deal that really works, that really protects the world from Iranian bad behavior, not just their nuclear program, but their missiles and their malign behavior as well". That's what we're going to do and I'll work hard with Europeans in next few days.
"The imbecile Trump's pretexts and insane move following a psychological war and breach of contract and unilateral pullout from the [nuclear deal] and his idiotic remarks against the powerful Iran revealed again the imperialistic nature of the criminal American leaders", one group of protesters in Tehran said in a statement.
"They were shifting the balance of power in the Middle East until President Trump got out of this deal". "The policy of the administration is to make sure that Iran never gets close to deliverable nuclear weapons".
Bolton struck a more hawkish tone with his comments in an interview with CNN's "State of the Union" than Pompeo did when he was interviewed on "Fox News Sunday". Britain, France, Germany, Russia and China are still signed on to the deal.
While he has committed to remaining in the nuclear agreement, French President Emmanuel Macron floated the idea of a supplemental deal on Iran during a recent visit to Washington. For president, who had that agreement in his sights since he was a candidate, it was a way of giving economic oxygen to regime in order to resume its arms race, despite all agreed inspection systems, as Allies argued.
As a private citizen, Bolton in the past has suggested that the United States push for a change in government in Iran.