On Thursday (local time), an Iranian missile destroyed a US Global Hawk surveillance drone, an incident that Washington said happened in international airspace. Trump later said he had called off a military strike to retaliate because it could have killed 150 people.
Tehran repeated on Saturday that the drone was shot down over its territory and said it would respond firmly to any US threat.
Speaking in Washington on Saturday before heading to the US presidential retreat at Camp David, Trump indicated the government was taking a diplomatic path to put pressure on Tehran by moving to impose new sanctions.
Military action was "always on the table," the president said, but he added that he was open to quickly reaching a deal with Iran that he said would bolster the country's flagging economy.
"We will call it 'Let's make Iran great again,'" Trump said.
He later wrote on Twitter from Camp David: "We are putting major additional Sanctions on Iran on Monday. I look forward to the day that Sanctions come off Iran, and they become a productive and prosperous nation again."
The Trump administration has sought to use promises of economic revival to solve other thorny foreign policy challenges, including the Israel-Palestinian peace process, with the White House outlining on Saturday a plan to create a global investment fund to lift the Palestinian and neighboring Arab state economies.
Both Trump and Tehran have said they are not seeking a war, but Iran has warned of a "crushing" response if attacked.
"Regardless of any decision they (US officials) make... we will not allow any of Iran's borders to be violated. Iran will firmly confront any aggression or threat by America," Foreign Ministry spokesman Abbas Mousavi told the semi-official Tasnim news agency on Saturday.
A senior commander of the elite Revolutionary Guards struck a similarly defiant note, in comments quoted by the Islamic Republic News Agency (IRNA).
"If the violation is repeated then our response will be repeated," said Brigadier General Amirali Hajizadeh, head of the Guards' aerospace division. "It's possible that this infringement of the Americans was carried out by a general or some operators."
Iran's foreign minister, Mohammad Javad Zarif, published a map on Twitter with detailed coordinates which he said showed the drone was flying over the Islamic Republic's territorial waters.
A Pentagon spokeswoman, Commander Rebecca Rebarich, said on Saturday: "We stand by where we said the aircraft was operating in international airspace."
Iran's Foreign Ministry summoned a United Arab Emirates envoy on Saturday because the UAE allowed the drone to be launched from a US military base on its territory, the Fars news agency reported.
Military sources told Reuters that US forces were getting ready to evacuate contractors from a military base in neighboring Iraq over "potential security threats," without saying what those threats might be. That was denied by Iraqi and US military spokesmen on Saturday.
Flights rerouted
Tensions in the region began to worsen significantly when Trump pulled out of a 2015 nuclear deal between Iran and six powers and reimposed sanctions on the country. The sanctions had been lifted under the pact in return for Tehran curbing its nuclear program.
The United States and Iran's main regional rival Saudi Arabia have also blamed Iran for attacks on two oil tankers last week in the Gulf of Oman and on four tankers off the United Arab Emirates on May 12.
Both incidents happened near the strategic Strait of Hormuz, a major conduit for global oil supplies. Iran has denied any involvement.
On Thursday, the Pentagon launched a long-planned cyber attack in retaliation for the oil tanker incidents, Yahoo News reported, citing former intelligence officials. The cyber strike disabled Iranian rocket launch systems, the Washington Post said on Saturday.
A Department of Defense spokeswoman said it would not comment on cyberspace operations, intelligence or planning.
World powers have called for calm and sent in envoys for talks to try to lower the temperature of a dispute that has pushed up the price of oil.
German Chancellor Angela Merkel called on Saturday for a political resolution of the crisis, adding: "That is what we are working on."
Britain's Foreign Office said Middle East minister Andrew Murrison would visit Tehran on Sunday to raise concerns about "Iran's regional conduct and its threat to cease complying with the nuclear deal."
Iran has threatened to breach the deal if the European signatories to the agreement fail to salvage it by shielding Tehran from US sanctions.
"The Europeans will not be given more time beyond July 8 to save the deal," Mousavi said, referring to Iran's deadline of 60 days that Tehran announced in May.
The US Federal Aviation Administration on Thursday issued an emergency order prohibiting US operators from flying in an oversea area of Tehran-controlled airspace over the Strait of Hormuz and Gulf of Oman. Some other international airlines are taking related precautions.
But Iran said on Saturday its airspace was "safe and secure" for all planes to cross, Tasnim reported.
Separately, Iran has executed a former contract employee for the aerospace organization of the Ministry of Defence on charges of spying for the US Central Intelligence Agency, the IRIB news agency reported on Saturday.
