President Trump ripped up what he called the “horrible one-sided” Iran nuclear deal Tuesday and vowed to reimpose crippling sanctions on the Islamic regime, leaving the world guessing what Tehran would do next and wondering whether the Middle East would be safer now or closer to war.

Mr. Trump said he quit the Obama-era agreement because it was “defective at its core.” He said the deal failed to stop Iranians from developing nuclear missiles and spreading terrorism throughout the region and wouldn’t prevent Tehran from pursuing nuclear breakout in 2025.

The bold move prompted Iran to threaten to fast-track a nuclear bomb, left America’s allies in Europe scrambling to hold the deal together and spurred bitter recriminations from Mr. Trump’s political foes at home.

The president, who has railed against the deal and threatened to kill it since his 2016 presidential campaign, was adamant.

“America will not be held hostage to nuclear blackmail,” he said in announcing the long-awaited decision at the White House. “We will not allow American cities to be threatened with destruction, and we will not allow a regime that chants ‘Death to America’ to gain access to the most deadly weapons on Earth.”

Mr. Trump was able to trash the agreement unilaterally because President Obama did not present it to the Senate for ratification, knowing that the Republican-controlled upper chamber likely would have rejected the secretively negotiated deal.

Many in Congress opposed terms of the deal. The bargain grew more irksome as it was revealed that the Obama administration paid Tehran $1.8 billion in cash as part of a secret side deal.

“This disastrous deal gave this regime — and it’s a regime of great terror — many billions of dollars, some of it in actual cash,” said Mr. Trump. “A great embarrassment to me as a citizen and to all citizens of the United States.”

Iranian President Hassan Rouhani almost immediately announced that he had ordered the foreign minister to open talks with the other parties in the 2015 nuclear deal: Britain, France, Germany, Russia and China.

If they couldn’t salvage the deal soon, he said, his country could “start enriching uranium more than before.”

“Iran is a country that adheres to its commitments, and the U.S. is a country that has never adhered to its commitments,” Mr. Rouhani said.

Mr. Trump warned that if Iran begins building nuclear bombs, it will have “bigger problems than it has ever had before.”

Mr. Trump signed a memorandum Tuesday that immediately reinstated sanctions on Iran. The Treasury will phase in some sanctions to allow U.S. individuals and companies to unwind financial ties with the Islamic republic.

Nobody should enter into new business deals with Iran, National Security Adviser John R. Bolton told reporters at the White House.

He was asked if Americans should view the withdrawal from the deal as a precursor for U.S. troops on the ground in Iran.

“They would be badly mistaken,” said Mr. Bolton.

It remained unclear what steps the U.S. would take beyond sanctions if Iran continues destabilizing activity by supporting terrorism or testing missiles.

The tough sanctions by the U.S., Europe and China brought Iran to the negotiation table. The 2015 deal lifted sanctions and allowed Iran to once again sell oil, which is the country’s economic lifeblood.

Since then, Iran has expanded its political and military influence in the Middle East, including contributing to violence and terrorism in Yemen and Syria.

Israeli Prime Minister Benjamin Netanyahu cheered Mr. Trump’s “courageous leadership” and said the “historic move” would make sure Iran never obtains nuclear weapons.

Israeli defense services were placed on high alert after Mr. Trump’s announcement, with officials citing unusual activity by Iranian forces in Syria.

British Prime Minister Theresa May, German Chancellor Angela Merkel and French President Emmanuel Macron issued a joint statement expressing “regret and concern” that Mr. Trump nixed the deal known as the Joint Comprehensive Plan of Action.

They urged the U.S. to not interfere with efforts by the other countries to continue enforcing the agreement, which allowed limited inspections of Iranian nuclear facilities by an international team and was supposed to halt Iran’s nuclear weapon breakout until 2025.

“There must be no doubt: Iran’s nuclear program must always remain peaceful and civilian,” they said.

The European leaders had been pressuring Mr. Trump not to quit the agreement. Mr. Macron and Ms. Merkel even made in-person pleas during visits to the White House last month.

Mr. Trump couldn’t be deterred.

“The United States no longer makes empty threats. When I make promises, I keep them,” he said.

Former President Barack Obama was livid that another piece of his legacy had been erased.

“Walking away from the JCPOA turns our back on America’s closest allies, and an agreement that our country’s leading diplomats, scientists and intelligence professionals negotiated,” he said in a lengthy statement. “The consistent flouting of agreements that our country is a party to risks eroding America’s credibility, and puts us at odds with the world’s major powers.”

Mr. Trump also pulled out of the Paris accord to fight climate change and the Trans-Pacific Partnership trade deal that the Obama administration negotiated.

Capitol Hill Democrats piled on scorn for what they viewed as Mr. Trump’s go-it-alone bluster on the world stage.

House Minority Leader Nancy Pelosi, California Democrat, hailed the Iran nuclear deal as a “great diplomatic achievement.”

“The president’s decision to follow his misguided and uninformed campaign promise to destroy the successful Joint Comprehensive Plan of Action endangers global security and defies comprehension,” Mrs. Pelosi said. “This rash decision isolates America, not Iran.”

However, Mr. Trump garnered plaudits from Republicans.

“President Trump is right to abandon the Obama administration’s bad deal,” said Senate Majority Whip John Cornyn, Texas Republican. “We know Iran has long thumbed its nose at the international community and has potentially violated this one-sided agreement. Any new agreement must prevent Iran from obtaining and employing weapons of mass destruction and be subject to congressional scrutiny.”

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