WASHINGTON — The United States and Iran exchanged escalating military threats on Friday as President Trump warned that he is “prepared to take whatever action is necessary’’ if Iran threatens Americans and Iran’s supreme leader, Ayatollah Ali Khamenei, vowed to exact vengeance for the killing on Trump’s order of Iran’s most valued general.

Although Trump insisted that he took the action to avoid a war with Iran, the continuing threats further rattled foreign capitals, global markets, and Capitol Hill, where Democrats demanded more information about the strike and Trump’s grounds for taking such a provocative and risky move without consulting Congress. Democrats also pressed questions about the attack’s timing and whether it was meant to deflect attention from the president’s expected impeachment trial this month in the Senate.

Speaking to reporters in a hastily arranged appearance at Mar-a-Lago, his Florida resort, Trump asserted that Major General Qassem Soleimani, who directed Iranian paramilitary forces throughout the Middle East, “was plotting imminent and sinister attacks on American diplomats and military personnel, but we caught him in the act and terminated him.’’

General Mark A. Milley, the chairman of the Joint Chiefs of Staff; Secretary of State Mike Pompeo; and Robert C. O’Brien, the national security adviser, echoed Trump’s remarks. But Milley, Pompeo, O’Brien, and other senior administration officials did not describe any new specific threats that were different from what American officials say Soleimani had been orchestrating for years.

In Baghdad, the State Department urged US citizens to leave Iraq immediately, citing “heightened tensions.’’ The US Embassy, which had been under siege by pro-Iranian protesters chanting “Death to America’’ in recent days, suspended consular operations. “US citizens should not approach the Embassy,’’ the State Department warned on Twitter.

At Fort Bragg, N.C., some 3,500 members of the 82nd Airborne, ordered to the Middle East this week, prepared to deploy to Kuwait.

On Wall Street, the stock market fell as oil prices jumped after the news of the general’s death. The price of Brent oil, the international benchmark, surged in the early hours of Hong Kong trading to nearly $70 a barrel — an increase of $3.

The immediate increase in the price of oil was among the largest since an attack on a critical Saudi oil installation in September that temporarily knocked out 5 percent of the world’s supply.

In more violence, another airstrike almost exactly 24 hours after the one that targeted Soleimani killed five members of an Iran-backed militia north of Baghdad, an Iraqi security official said. The Iran-backed Popular Mobilization Forces confirmed the strike, saying it hit one of its medical convoys near the stadium in Taji, north of Baghdad. The group said none of its top leaders were killed. A US official speaking on condition of anonymity said the attack was not an American military attack.

Trump said that the killing early Friday of Soleimani, the commander of the Quds Force branch of Iran’s Revolutionary Guard, was long overdue. He insisted he did not want a larger fight with Iran.

“We took action last night to stop a war,’’ the president said. “We did not take action to start a war.’’ But he also warned Iran that the American military had “already fully identified’’ potential targets for further attacks “if Americans anywhere are threatened.’’

Hours earlier, Khamenei issued his own warning to Trump about Soleimani’s death from a missile fired by an American MQ-9 Reaper drone at the general’s convoy at Baghdad International Airport.

“His departure to God does not end his path or his mission,’’ Khamenei said in a statement, “but a forceful revenge awaits the criminals who have his blood and the blood of the other martyrs last night on their hands.’’

Pompeo, an Iran hawk, said a planned attack on Americans had been “imminent’’ before the strike.

Writing on Twitter earlier in the day, Trump suggested that Soleimani “got caught’’ preparing to hit American targets.

“General Qassem Soleimani has killed or badly wounded thousands of Americans over an extended period of time, and was plotting to kill many more . . . but got caught!’’ Trump tweeted. “He was directly and indirectly responsible for the death of millions of people, including the recent large number of PROTESTERS killed in Iran itself.’’

The strike touched off an immediate debate in Washington, with Republicans hailing the action as a decisive blow against a longtime enemy with American blood on his hands and Democrats expressing concern that the president was risking a new war in the Middle East.

With Congress returning to town after the holidays for a presumed Senate impeachment trial, Trump risked suspicion that he was taking action overseas to distract from his political troubles at home, a la the movie “Wag the Dog.’’

As a private citizen, Trump repeatedly accused President Barack Obama of preparing to go to war with Iran to bolster his reelection chances in 2012. As president, Trump has questioned his own intelligence agencies and peddled repeated falsehoods, a record that could undermine the administration’s credibility on the highly delicate subject.

Democratic leaders complained that Trump acted without consulting or even telling Congress first. The president responded by retweeting a post comparing Senator Chuck Schumer of New York, the Democratic leader, to the Iranians.

Senator Mitch McConnell of Kentucky, the Republican leader, said that a classified briefing was being arranged for all senators next week and that everyone should welcome the demise of Soleimani. “For too long, this evil man operated without constraint and countless innocents have suffered for it,’’ McConnell said on the floor. “Now his terrorist leadership has been ended.’’

Democrats said Trump was playing a dangerous game that could further involve the United States in Middle East conflict rather than pull out as he has promised. “President Trump came into office saying he wanted to end America’s wars in the Middle East, but today we are closer to war with Iran than ever before and the Administration’s reckless policy over the last 3 years has brought us to the brink,’’ Senator Chris Van Hollen of Maryland wrote on Twitter.

Soleimani, the driving force behind Iranian-sponsored attacks and operations over two decades around the region including Iraq, Syria, Yemen, and Lebanon, was considered perhaps the second-most powerful figure in Iran.

In an unusual move, the ayatollah attended an emergency meeting of the Supreme National Security Council. “America must know the criminal attack on Soleimani was its worst strategic mistake in the Middle East and that America will not escape the consequences easily,’’ the council said afterward. “As our Supreme Leader said in his message, a harsh revenge awaits the criminals who have the general’s blood on their hands. These criminals will face revenge at the right time and place.’’

Pompeo said in a TV appearance that the United States had intelligence that Soleimani was preparing a specific, new operation to target Americans in the Middle East, but declined to elaborate.

“He was actively plotting in the region to take actions, a big action as he described it, that would have put dozens if not hundreds of American lives at risk,’’ Pompeo said on CNN. “It was imminent.’’

The decision to hit Soleimani complicates relations with Iraq’s government, which has tried to balance itself between the United States and Iran.

A senior Iraqi official said Friday that there was a good chance the Iraqi Parliament would vote to force US troops to leave Iraq.

Material from the Associated Press was included in this report.