President Donald Trump warned Iran early on Monday not to threaten the United States again or it'll face its "official end," shortly after a rocket landed near the US Embassy in Baghdad overnight.

Trump's tweet comes after he seemingly sought to soften his tone on Iran following days of heightened tension sparked by Washington's sudden deployment 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. Houthi rebels launched a drone attack on an oil pipeline in Saudi Arabia. US diplomats relayed a warning that commercial airlines could be misidentified by Iran and attacked.

All these tensions are the culmination of Trump's decision a year ago to pull America 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.

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The tweet from Trump early on Monday came 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 US Embassy, causing no injuries.

Iraqi military spokesman Brig. Gen Yahya Rasoul told The Associated Press that the rocket was believed to have been fired from east Baghdad.

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

Trump campaigned on pulling the US 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 withdrawal, the US 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 allow it to build atomic bombs.

In an interview aired on Sunday on the Fox News Channel, 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," Trump said.

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

In Saudi Arabia, the kingdom's military intercepted two missiles fired by the Houthi rebels in neighbouring Yemen.

The missiles were intercepted over the city of Taif and the Red Sea port city of Jeddah, the Saudi-owned satellite channel Al-Arabiya reported. The channel cited witnesses for the 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 recognised government.

Between the two targeted cities is Makkah. Many pilgrims are now in the city amid the holy month of Ramazan.

Meanwhile, the US 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.