Iran's President Rohani says he will try to maintain a deal that works for his country but his threat was clear: if negotiations are unsatisfactory, Iran will recommence full uranium enrichment. European leaders, meanwhile, urge calm and restraint.
It came as no real surprise, not least because Trump had basically announced it on twitter beforehand, but the US President announced on Tuesday that the US would be pulling out of the Iran nuclear deal and reimposing "full sanctions" on a regime he described as "monstrous".
How has the world reacted?
President Hassan Rouhani was quick to make a statement that, whilst broadly measured and conciliatory in tone, nonetheless threatened full scale Iranian nuclear armament depending on the nature of the global response over the coming days.
He described Trump's decision as "psychological warfare" but said that was a war the US would not be able to win. He also took a swipe at Donald Trump, saying that the US never kept to its international obligations and that he "felt sorry for" US citizens.
The Iranian President said that his country would enter into negotiations with the European partners to the deal, as well as with Russia and China, but that, if the outcome was unsatisfactory, Iran was ready to turn to "insdustial levels" of uranium enrichment.
High Representative/Vice President Federica Mogherini said that the EU regretted Trump's statement. However, she also sought to play down the implications of the decision, stating that "the nuclear deal is not a bilateral agreement and it is not in the hands of any single country to terminate it unilaterally".
Mogherini said that the European Union would retain its commitment to the agreement for as long as Iran kept to its side of the deal. The concern that she expressed about Trump's reimposition of tough sanctions, including against companies from third party countries continuing to trade with Iran, is an indicator of just how tough sticking to that commitment may prove to be.
Macron, May and Merkel
The three European signatories to the deal, France, the UK and Germany, put out a joint statement also expressing regret about Trump's decision. They emphasised their "continuing commitment" to the deal, stating that, contrary to the comments made by Trump, Iran continued to abide by its terms.
There was a note of caution, however, as the leaders affirmed that "Iran's nuclear programme must always remain peaceful and civilian" and raised concerns about issues needing to be addressed, including the sunset clause, Iran's ballistic missile programme. and its "destabilising regional activities".
Israel claims that its position on Iran has been vindicated by Donald Trump's announcement. Prime Minister Benjamin Netanyahu publicly thanked the US President for his decision.
He also said that "everybody recognizes the malign intentions of Iran, and I think everybody also recognizes Israel's right of self-defense, which is really our common defense".
Meanwhile Israeli military sources claimed evidence of increased Iranian military activity in Syria, causing it to reinforce its defences in Golan Heights.
Saudi Arabia, which is essentially engaged in a proxy war with Iran in Yemen, was also quick to welcome Donald Trump's decision.
An official statement from the Kingdom said that Iran had used the deal "to continue its destabilizing activities in the region, especially through the development of ballistic missiles, and its support for terrorist groups in the region".
Russia, one of the signatories to the deal, has not yet issued an official reaction to Trump's announcement. However, before the White House press conference the Kremlin had warned of "harmful consequences" if the US decided to withdraw from the Iran nuclear deal.
At home in the US
No more surprising than Trump's announcement was former President Obama's reaction to it.
Whilst those on the left have stated that the US withdrawal leaves the country vulnerable, those on the right tend to agree with Donald Trump that US citizens are safer out than in.