Dubai, United Arab Emirates -- President Trump warned Iran early on Monday not to threaten the United States again or it would face its "official end," shortly after a rocket landed near the U.S. Embassy in Baghdad overnight.

Mr. Trump's tweet came after he seemingly sought to soften his tone on Iran following days of heightened tension sparked by the sudden deployment by the U.S. of bombers and an aircraft carrier to the Persian Gulf over still-unspecified threats.

In the time since, officials in the United Arab Emirates allege four oil tankers sustained damage in a sabotage attack. Yemeni rebels allied with Iran launched a drone attack on an oil pipeline in Saudi Arabia. U.S. diplomats relayed a warning that commercial airlines could be misidentified by Iran and attacked, something dismissed by Tehran.

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All the tensions are the culmination of Mr. Trump's decision a year ago to pull the U.S. out of Tehran's nuclear deal with world powers. And while both Washington and Tehran say they don't seek war, many worry any miscalculation at this fraught moment could spiral out of control.

Mr. Trump's tweet has already been met with reaction out of Tehran, with Iranian Foreign Minister Javad Zarif tweeting that the U.S. president hopes to achieve what "other aggressors" like violent Mongolian ruler Genghis Khan "failed to do."

Goaded by #B_Team, @realdonaldTrump hopes to achieve what Alexander, Genghis & other aggressors failed to do. Iranians have stood tall for millennia while aggressors all gone. #EconomicTerrorism & genocidal taunts won't "end Iran". #NeverThreatenAnIranian. Try respect—it works! — Javad Zarif (@JZarif) May 20, 2019

"Iranians have stood tall for millennia while aggressors all gone. Economic Terrorism & genocidal taunts won't 'end Iran,'" Zarif added.

Mr. Trump's early Monday tweet was posted just hours after a Katyusha rocket fell in Baghdad's heavily fortified Green Zone near the statue of the Unknown Soldier, less than a mile from the U.S. Embassy, causing no injuries. Iraqi military spokesman Brig. Gen. Yahya Rasoul told The Associated Press the rocket was believed to have been fired from east Baghdad. The area is home to Iran-backed Shiite militias.

Later, Iraqi forces said they recovered the rocket in front of the Technological university in Baghdad.

The Reuters news agency reported the blast was heard across central Baghdad and pointed out that the embassy and U.S. consulate in the Iraqi Kurdish regional capital of Erbil had already moved out non-emergency staffers "out of apparent concern about perceived threats from Iran."

Mr. Trump tweeted, "If Iran wants to fight, that will be the official end of Iran. Never threaten the United States again!" The president didn't elaborate, nor did the White House.

Hours later, two influential Shiite figures in Iraq warned about pulling their country into a war between the United States and Iran, saying it would turn Iraq into a battlefield and inflict much harm.

Iraq's populist Shiite cleric Moqtada al-Sadr said in a statement on Monday that any political party that would involve Iraq in a U.S.-Iran war "would be the enemy of the Iraqi people," and Qais al-Khazali, the leader of an Iranian-backed group, said he is opposed to operations that "give pretexts for war."

Trump ally Sen. Lindsey Graham meanwhile tweeted that he personally received a briefing from the president's National Security Advisor John Bolton about escalating tensions with Iran, remarking that "It is clear that over the last several weeks Iran has attacked pipelines and ships of other nations and created threat streams against American interests in Iraq."

Just received a briefing from National Security Advisor Bolton about escalating tensions with Iran. It is clear that over the last several weeks Iran has attacked pipelines and ships of other nations and created threat streams against American interests in Iraq. — Lindsey Graham (@LindseyGrahamSC) May 20, 2019

"The fault lies with the Iranians, not the United States or any other nation. If the Iranian threats against American personnel and interests are activated we must deliver an overwhelming military response. Stand firm Mr. President," Graham later encouraged the president.

Mr. Trump campaigned on pulling the U.S. from the 2015 nuclear accord, which saw Iran agree to limit its enrichment of uranium in exchange for the lifting of economic sanctions. Since the U.S. withdrawal, Washington has re-imposed previous sanctions and come up with new ones, as well as warned nations around the world they would be subject to sanctions as well if they import Iranian oil.

Iran just announced it would begin backing away from terms of the deal, setting a 60-day deadline for Europe to come up with new terms or it would begin enriching uranium closer to weapons-grade levels. Tehran long has insisted it does not seek nuclear weapons, though the West fears its program could enableit to build atomic bombs.

In an interview aired Sunday on the Fox News Channel, Mr. Trump called the nuclear deal a "horror show."

"I just don't want them to have nuclear weapons and they can't be threatening us," Mr. Trump said.

However, the nuclear deal had kept Iran from being able to acquire enough highly enriched uranium for a bomb. U.N. inspectors repeatedly certified that Iran was complying with the accord.

In Saudi Arabia, the kingdom's military said it intercepted two missiles fired by the Houthi rebels in neighboring Yemen. The missiles were intercepted over the city of Taif and the Red Sea port city of Jiddah, the Saudi-owned satellite channel Al-Arabiya reported.

The channel cited witnesses for its information. The Saudi government has yet to acknowledge the missile fire, which other Saudi media also reported. Hundreds of rockets, mortars and ballistic missiles have been fired into the kingdom since a Saudi-led coalition declared war on the Houthis in March 2015 to support Yemen's internationally recognized government.

Between the two targeted cities is Mecca, home to the cube-shaped Kaaba that Muslims pray toward five times a day. Many religious pilgrims are now in the city amid the Muslim holy fasting month of Ramadan.

Meanwhile, the U.S. Navy's 5th Fleet on Sunday announced it would begin "enhanced security patrols" in international waters with members of the Gulf Cooperation Council, which includes Bahrain, Kuwait, Oman, Qatar, Saudi Arabia and the United Arab Emirates.

Already, the USS Abraham Lincoln aircraft carrier, the amphibious assault ship USS Kearsarge and others are in the Arabian Sea, waters close to the Strait of Hormuz, the narrow mouth of the Persian Gulf through which a third of all oil traded at sea passes.