Trump's announcement that a decision was imminent cut short a last-ditch European diplomatic drive to save the accord ahead of what had been a May 12 deadline.
Trump had until Saturday to decide whether to renew a waiver on one package of US sanctions targeting Iran's oil sector that had been lifted as part of Washington's commitment under the 2015 deal.
"I will be announcing my decision on the Iran Deal tomorrow from the White House at 2:00 pm (1800 GMT)," the president said in a tweet.
The president may now also decide to announce the fate of the rest of Washington's nuclear-related sanctions, which are covered by different waivers, and effectively undermine the entire accord, reached between Tehran and six world powers.
European leaders and diplomats -- including Britain's Foreign Secretary Boris Johnson, who was in Washington on Monday -- have been pleading with the United States to retain the core of what Trump called the "flawed" accord.
And even if, as now seems inevitable, Trump pulls Washington out of the agreement, Britain, France, Germany, Russia and China may decide to stay in and to urge Tehran to maintain its own commitments.
But if Trump's decision raises the prospect of renewed US sanctions on European firms and banks doing business with Iran, the accord itself will be in peril -- amid mixed signals from Tehran.
Some Iranian leaders have signalled they might seek to rapidly restore the enrichment capabilities they surrendered under the deal, and European capitals fear Tehran may resume the hunt for a bomb.
Tehran has long insisted it has no ambition to build nuclear weapons, but the signatories to the deal never believed them, and supporters of the accord have warned of a Middle East arms race if it fails.
And they are skeptical that Trump's administration has a back-up plan to restrain Iranian ambitions once he has made good on his campaign promise to tear up a deal endorsed by his predecessor Barack Obama.
Britain's Johnson, who was in Washington to lobby Secretary of State Mike Pompeo and Vice President Mike Pence, told Fox News: "Plan B does not seem to be, to me, particularly well-developed at this stage."
Given the multinational nature of the deal, nothing the so-called EU three -- Britain, France and Germany -- can do would allow them to rewrite it, but they have promised to work on a powerful supplemental agreement.
But so far, all signs point to Trump making good on his threat.
German Foreign Minister Heiko Maas warned the accord's collapse could spark "an escalation" in the region and stressed that Washington's European allies think the deal "makes the world a safer place."
His French counterpart Jean-Yves Le Drian, on a visit to Berlin, said the agreement is "the right way to stop Iran from getting access to nuclear weapons" and "will save us from nuclear proliferation."
Under the landmark nuclear pact, Iran agreed to scale back nuclear enrichment and put its program under international supervision in return for international sanctions relief.
Trump has consistently complained about the agreement, reached under Obama, citing as its shortcomings certain clauses such as the "sunset" provisions lifting some nuclear restrictions on Tehran from 2025.
In an attempt to salvage the deal, French President Emmanuel Macron has pushed to extend its scope to address this issue, as well as Iran's missile capabilities and its role in the region.
Iran's support for Syrian President Bashar al-Assad, the Lebanese armed group Hezbollah in Syria's civil war and Shiite Huthi rebels in Yemen have added to tension between Tehran and Western powers.
Iran's President Hassan Rouhani on Sunday issued a strong warning to the United States not to quit the pact.
"If the United States leaves the nuclear agreement, you will soon see that they will regret it like never before in history," Rouhani said.
He also vehemently reiterated his country's opposition to curtailing its non-nuclear missile capabilities, insisting Tehran "will build as many missiles and weapons as needed."
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