Pompeo, in interviews on Fox News and CNN, declined to discuss many details of the alleged threat but said it was "an intelligence based assessment" that drove the decision to target Soleimani.
US officials said Washington was sending nearly 3,000 more troops to the Middle East amid rising threats to US forces there, joining roughly 750 forces sent to Kuwait this week.
In a tweet, Trump said Soleimani had "killed or badly wounded thousands of Americans over an extended period of time, and was plotting to kill many more", but did not elaborate.
The attack also killed top Iraqi militia commander Abu Mahdi al-Muhandis, an adviser to Soleimani. Their deaths divided Iraqi opinion. Many condemned the attacks, seeing Soleimani as a hero for his role in defeating Islamic State. Others voiced approval, saying Soleimani and Muhandis had backed the use of force against unarmed anti-government protesters last year and set up the militias they blame for many of Iraq's social and economic woes.
However, many Iraqis criticised Washington for killing the men on Iraqi soil and possibly plunging the country into a war. The attack followed a sharp increase in US-Iranian hostilities last week when pro-Iranian militiamen attacked the US embassy in Baghdad following a US air raid on the Kataib Hezbollah militia, founded by Muhandis. Iraq's prime minister said with Friday's attack Washington had violated a deal for keeping US troops in his country.
CONCERN OVER ESCALATION
Khamenei said a harsh revenge awaited the "criminals" who killed Soleimani and his death would redouble resistance against the United States and Israel. He called for three days of national mourning and appointed Soleimani's deputy, Brigadier General Esmail Ghaani, to replace him as Quds Force head.
Iran summoned a Swiss envoy for a second time to reply to a US message, Iranian media said, hours after a Swiss diplomat delivered a US communication over the killing.
The killing was an act of "international terrorism," Foreign Minister Mohammad Javad Zarif said. US officials said Soleimani was killed in a drone strike. Iran said he died in an attack by US helicopters. Israel put its army on high alert and US allies in Europe including Britain, France and Germany voiced concerns. U.N. Secretary-General Antonio Guterres called for "maximum restraint". Iran's top Arab foe, Saudi Arabia, urged restraint.
The US embassy in Baghdad urged American citizens to leave Iraq immediately. Dozens of US citizens working for foreign oil companies in the southern city of Basra were leaving the country. Iraqi officials said the evacuations would not affect output and exports.
Oil prices jumped more than $3 a barrel over concern about disruption to Middle East supplies. In New York City, officials went on heightened alert for possible Iranian retaliation, the mayor said. In Beirut, the US embassy urged Americans in Lebanon to be highly vigilant, a security alert on its website said.
'STICK OF DYNAMITE'
Trump critics called the operation reckless. "President Trump just tossed a stick of dynamite into a tinderbox," said former Vice President Joe Biden, a contender in this year's US presidential election. Chas Freeman, a retired US ambassador, said he could think of no other example of the United States openly killing a senior foreign government official during peacetime. "In times of peace? Never. This is unprecedented," Freeman said.
As chief of the Quds Force, the Revolutionary Guards foreign arm, Soleimani had a key role in fighting in Syria and Iraq. Over two decades he was at the forefront of projecting the Islamic Republic's military influence across the Middle East, acquiring celebrity status at home and abroad.
President Hassan Rouhani said the killing would stiffen Iran's resistance to the United States. The Revolutionary Guards said anti-US forces would exact revenge in the Muslim world. Hundreds of Iranians marched toward Khamenei's compound in Tehran to convey their condolences.
"I am not a pro-regime person but I liked Soleimani. He was brave and he loved Iran, I am very sorry for our loss," said housewife Mina Khosrozadeh in Tehran. In Soleimani's home town, Kerman, people wearing black gathered in front of his father's house, crying as they listened to a recitation of verses from the holy Quran.
"Heroes never die. It cannot be true. Qassem Soleimani will always be alive," said Mohammad Reza Seraj, a teacher. Iraqi Prime Minister Adel Abdul Mahdi said the killings breached Iraq's sovereignty and would lead to war. Israel has long seen Soleimani as a threat and Prime Minister Benjamin Netanyahu backed the US action. Israeli Army Radio said the military was on heightened alert. Russia called the killing a "short-sighted" step that would lead to escalations in the region.
PREVIOUS ATTACKS
The slain commander's Quds Force, along with battle-hardened paramilitary proxies in the region, has ample means to respond. In September, US officials blamed Iran for a missile and drone attack on oil plants of energy giant Saudi Aramco. Washington has also blamed Tehran for raids on Gulf shipping.
Iran has denied responsibility for the strikes and accused Washington of warmongering by reimposing crippling sanctions on Iran's main export, oil, in order to force Tehran to renegotiate a deal to freeze its nuclear activities. Soleimani had survived several assassination attempts by Western, Israeli and Arab agencies over the past two decades. Soleimani became head of the force in 1998, after which he quietly strengthened Iran's ties with Hezbollah in Lebanon, Syria's government and Shia militia groups in Iraq.