Bolton said Europe was still digesting the May 8 move by Trump that has the United States dropping out of the 2015 agreement with Tehran.
But because the European Union and other intentional players have chose to stick with the deal, US sanctions are likely to affect only up to around 350,000 barrels a day, once reinstated within six months' time, according to analysts at MUFG Bank.
Trump's Iran announcement came earlier than expected - four days ahead of a May 12 deadline - and he made a point of mentioning that Secretary of State Mike Pompeo was on his way to North Korea "at this very moment".
Iran said it had asked Europe's Airbus to announce whether it would go ahead with a plane deal with Tehran following the USA pullout.
The 2015 agreement between major powers and Iran set limits on its nuclear activities in exchange for the lifting of sanctions. "The Treasury Department thanks the UAE for its close collaboration on this matter".
President Trump's decision to withdraw the USA from the Iran deal has lots of diplomatic consequences.
Oil prices surged following President Trump's withdrawal from the Iran nuclear deal.
Adel Al-Jubeir, speaking to CNN, said Saudi Arabia would seek to develop its own nuclear weapons capacity should Iran do the same.
"What the full impact on Iranian flows will be is still hard to estimate", Petromatrix strategist Olivier Jakob said.
Daily July Brent Crude
On the bullish side of the coin, the US plans to re-impose sanctions against Iran, which produces around 4 percent of global oil supplies. If the deal cannot be fixed, the United States could no longer be a party to it.
Crude oil prices settled lower today, easing off three-and-a-half year highs, but completed back-to-back weekly gains, sparked by uncertainty over how much oil the global market will lose following the USA decision to reimpose sanctions on Iran.
Investors seem to price in the fact that a USA decision to reimpose sanctions on Iran is helping China's recently established crude oil futures, and may encourage efforts to start trading oil in Yuan instead of dollars.
The Organisation of Petroleum Exporting Countries, as well as Russian Federation, have already slashed their oil production over the past 12 months to revive the commodity's futures after Brent crude prices slumped to about $US45 a barrel in June a year ago.
While the U.S. could "totally d***" the Iranians, it would requires over a "couple of million" men, led to unspeakable causalities and require a full-scale invasion of Iran.
One factor that could prevent markets from tightening further is soaring US oil output.
A spokesman for Mrs May said: "The Prime Minister reiterated the Government's position on the Iran nuclear deal, noting that we and our European partners remain firmly committed to ensuring the deal is upheld, as the best way of preventing Iran from developing a nuclear weapon".
Oil extended gains above $71/bbl on the risk of supply disruptions as a conflict between Israel and Iran ratcheted up, and after the US renewed sanctions on OPEC's third-largest producer.
Yet the team at Capital Economics doesn't believe Mr. Trump's withdrawal will be a big deal for oil prices in the end.