World leaders were quick to react to US President Donald Trump's decision to "decertify" an international deal on Iran's nuclear programme.

The 2015 deal, reached between Iran and the United States, Britain, France, Germany, Russia and the European Union, saw Tehran curtailing its nuclear programme in exchange for the easing of crippling economic sanctions.

In a White House address on Friday, Trump struck a blow against the accord in defiance of other world powers, and despite the UN nuclear watchdog's repeated confirmations that Iran was complying with its obligations under 2015's Joint Comprehensive Plan of Action (JCPOA).

Trump's move does not amount to a withdrawal from the deal, but instead pushes action to US Congress, which could reimpose sanctions that were lifted under the pact.

He threatened, however, that if a deal could not be reached with Congress or US allies, he would walk away from the accord.

Trump's speech put him at odds with US allies in Europe, as well as Iran and Russia, with leaders saying they would stick by the landmark pact.

"We encourage the US Administration and Congress to consider the implications to the security of the US and its allies before taking any steps that might undermine the JCPOA, such as re-imposing sanctions on Iran lifted under the agreement," French President Emmanuel Macron, German Chancellor Angela Merkel and British Prime Minister Theresa May said in a joint statement.

In Brussels, Federica Mogherini, the EU foreign policy chief, said the Iran deal is an international agreement and "it is not up to any single country to terminate it."

She added: "It is not a bilateral agreement, it does not belong to any single country ... The president of the United States has many powers, but not this one."

In a statement after Trump's speech, Russia's foreign ministry said there was no place in international diplomacy for "threatening" and "aggressive" rhetoric, adding that such methods were doomed to fail.

"It is a hangover from the past, which does not correspond to modern norms of civilised dealings between countries," the statement said.

"We viewed with regret the decision of the US President not to confirm to Congress that Iran is fulfilling in good faith" the nuclear deal, it added.

The ministry said Trump's decision to de-certify the deal would not have a direct impact on the implementation of the agreement, but that it ran counter to its spirit.

OPINION: What Trump's decision on Iran will mean for the world

For his part, Iranian President Hassan Rouhani hit back at Trump's new strategy on Iran.

"What was heard today was nothing but the repetition of baseless accusations and swear words that they have repeated for years," Rouhani said in a televised address from Tehran.

"The Iranian nation does not expect anything else from you," he added.

Rouhani said that despite the US president's aggressive rhetoric, Tehran remained committed to the nuclear agreement for the time being.

"We respect the JCPOA ... so long as it remains in keeping with our national rights and interests," he said.

'Most robust nuclear verification regime'

United Nations Secretary-General Antonio Guterres "very much hopes" the nuclear deal with Iran can be salvaged, his spokesman said.

Stephane Dujarric said Guterres considers the deal to be a "very important breakthrough to consolidate nuclear non-proliferation and advance global peace and security".

"The secretary-general very much hopes that it will remain in place," Dujarric added.

Also reacting to Trump's speech, Yukiya Amano, chief of the UN atomic watchdog, reiterated that Iran was under the world's "most robust nuclear verification regime".

"The nuclear-related commitments undertaken by Iran under the JCPOA are being implemented," said Amano, director general of the International Atomic Energy Agency.

In Washington, DC, Nancy Pelosi, the top Democrat in the House, called Trump's move "a grave mistake" that threatens the country's security and credibility.

Pelosi said Trump ignored "the overwhelming consensus of nuclear scientists, national security experts, generals and his own cabinet, including, reportedly, his secretary of defense and secretary of state".

Defence Secretary Jim Mattis told a Senate committee last week that it is in the US' national security interests to stay a part of the international accord.

Pelosi said Washington's allies in Europe have no intention of leaving the seven-nation pact, adding that if Trump's judgment leads to an unravelling of the deal, it will be the US that's isolated, not Iran.

Israel, Saudi Arabia praise Trump

Trump, however, got support from Israel and Saudi Arabia.

"President Trump has just created an opportunity to fix this bad deal, to roll back Iran's aggression and to confront its criminal support of terrorism," Israeli Prime Minister Benjamin Netanyahu said in a video statement.

Saudi Arabia also welcomed what it called Trump's "decisive strategy" towards Iran and alleged lifting sanctions had allowed Tehran to develop its ballistic missile programme, step up its support for groups including Hezbollah and Houthi rebels in Yemen, and attack global shipping lanes.

The Riyadh government said in a statement it had supported the nuclear agreement, "but Iran took advantage of the economic gain from raising sanctions and used it to continue destabilising the region."

It said it would continue to work with allies to achieve the goals announced by Trump and end Iran's "hostile activities".