President Donald Trump on Monday signed an executive order putting in place what he called "hard-hitting" new sanctions on Iran.

"We will continue to increase pressure on Tehran,” Trump told reporters in the Oval Office, adding that the announcement "follows a series of aggressive behaviors by the Iranian regime in recent weeks" — including the downing of a U.S. drone.

"The Supreme Leader of Iran is one who ultimately is responsible for the hostile conduct of the regime," Trump said.

The new sanctions, Trump said, will deny Supreme Leader Ayatollah Ali Khamenei and other top leaders within the regime access to "key financial resources and support."

The fresh round of sanctions came after Iran shot down a U.S. military drone over what the U.S. has said was international waters.

Trump had said Friday that he had been "cocked and loaded" to retaliate by striking Iranian targets but deemed that the loss of life would be disproportionate to the downing of an unmanned U.S. drone.

Trump said Monday that the sanctions were a "strong and proportionate response" to Iran’s actions and promised to "continue to increase pressure on Tehran until the regime abandons its dangerous activities and its aspirations, including the pursuit of nuclear weapons."

But, he added, the U.S. does "not seek conflict with Iran" and that he looks "forward to discussing whatever I have to discuss with anybody that wants to speak."

The drone strike and the aborted decision to strike Iranian targets followed weeks of rising tension and attacks on two oil tankers in the Gulf last week. The developments are underpinned by a deep mutual mistrust between the nations, as well as U.S. criticism of Iran's nuclear and ballistic missile activities and support for proxies in various Middle East conflicts.

Earlier Monday, Iran said it could shoot down another U.S. drone if necessary.

"Everyone saw the downing of the unmanned drone," Iran's navy commander, Rear Admiral Hossein Khanzadi, told the Tasnim news agency, according to a translation by Reuters. "I can assure you that this firm response can be repeated, and the enemy knows it."

Brian Hook, the U.S. special representative for Iran, revealed Monday that Washington is hoping to start an international "new initiative to enhance maritime security," following several attacks on tankers in the Gulf of Oman that Washington blames on Tehran. Iran has denied any involvement in the incidents.

Hook was speaking on a call with reporters from Muscat, Oman, the fourth stop on his Middle East tour. He did not provide details of the proposed scheme but said the G-20 summit this week in Osaka, Japan, would be the perfect forum in which to discuss the idea further.

The U.S. says it wants to re-enter negotiations with Iran. But an adviser to the Iranian president said his country would not do so unless the U.S. lifts sanctions, which were reimposed by Trump after he withdrew from the landmark nuclear deal signed under the administration of President Barack Obama in 2015.

Iran was complying with the deal's terms, which limited its nuclear activities in return for lifting international sanctions. Trump has always hated the deal, saying it did not properly address Iran's growing influence in the region and ballistic missiles program.

On Monday, Hesameddin Ashena, an adviser to President Hassan Rouhani, tweeted that if the U.S. expects Iran to go beyond its terms of this deal, Washington, too, must offer concessions of its own.

"U.S. offer for negotiations with no precondition is not acceptable while sanctions and threats continue," Ashena wrote, according to a Reuters translation. "If they want something beyond the JCPOA, they should offer something beyond the JCPOA; with international guarantees," he added, referring to the nuclear deal's official name, the Joint Comprehensive Plan of Action.

Under Trump, the U.S. military has drastically stepped up its secret hacking of foreign computer networks in a new effort to keep Iran and other countries, such as China and Russia, on their heels, current and former U.S. officials have told NBC News.

However, Iran's telecoms minister said that while the U.S. had launched a long-planned cyberattack to disable his country's rocket launch systems, it was unsuccessful.

"They try hard, but have not carried out a successful attack," Mohammad Javad Azari Jahromi, Iran's minister for information and communications technology, said on Twitter, according to a translation by Reuters.

The tensions looked set to dominate Secretary of State Mike Pompeo's visit Monday to Saudi Arabia, one of Iran's regional enemies.

Pompeo met with King Salman although their discussion was closed to the press. The secretary of state told reporters ahead of his trip Sunday that "significant" sanctions would be announced against Iran, adding to those that the U.S. says are already squeezing its economy.

Protesters gather in front of the White House last week to speak out against any potential conflict with Iran. Tasos Katopodis / Getty Images

"We are going to deny them the resources they need" to allegedly fund militant groups in the region, "thereby keeping American interests and American people safe all around the world," Pompeo said.

The secretary of state is also expected to meet Crown Prince Mohammed bin Salman in the Saudi city of Jiddah, before heading to Abu Dhabi, the United Arab Emirates, another close U.S. ally and partner.

Meanwhile, John Bolton, the national security adviser, was in Israel, another of Iran's staunch foes, saying that the airstrikes Trump halted could be revived if necessary, and that no one had given Iran a "hunting license in the Middle East."

Tensions among Washington, its allies and Tehran have soared under the Trump administration, coming to a head last week when Iran shot down a U.S. surveillance drone. It said the aircraft was in its airspace, while the U.S. claims it was in international airspace.

Trump then called off airstrikes on three Iranian targets with minutes to spare, a decision he said was motivated after he was advised that an estimated 150 people would die in the operation.

Alexander Smith reported from London, Abigail Williams reported from Washington, and Adam Edelman reported from New York.