WASHINGTON — President Donald Trump leveled new sanctions on Iran Monday saying America does not seek conflict, adding: “Never can Iran have a nuclear weapon.”

Speaking with reporters in the Oval Office, Trump said he had signed an executive order imposing “hard hitting” sanctions on Iran’s most senior leader, military officials and its top diplomat, Foreign Minister Javad Zarif.

Less than a week after Iran shot down a U.S. surveillance drone and Trump aborted a retaliatory strike, Trump warned, “We will continue to increase pressure on Tehran.”

Trump and his top foreign policy aides hope to pressure Iran’s leaders to limit their nuclear program and to ramp down both its military activity and support for militants in the Mideast. But Democratic lawmakers and foreign policy experts have warned the strategy will only provoke Iranian leaders into a violent response.

Reuters reported that Iranian hardline media said Monday the new U.S. sanctions imposed on Tehran were based on “fabricated excuses,” but Iranian officials had not immediately responded.

Meanwhile, U.S. Secretary of State Mike Pompeo held talks Monday with the Saudi king and crown prince about countering the military threat from Iran by building a broad, global coalition that includes Asian and European countries.

Pompeo is expected to have a tough time convincing European allies. Germany, France and Britain, as well as Russia and China, remain part of the nuclear accord that lifted sanctions on Iran in exchange for set limits on its uranium enrichment levels. Trump pulled the U.S. out of the deal last year.

House Speaker Nancy Pelosi, D-Calif., said last week she was very, very concerned” about the possibility of a miscalculation” and criticized the Trump administration for abandoning the multi-national nuclear deal with Iran. She cautioned against provoking Iranian leaders to further violence.

Days after the U.S. accused Iran of striking two tankers in the strategic Strait of Hormuz, Trump tweeted Monday that China and Japan depend on the security of the Persian Gulf waterways for the bulk of their oil imports. He asked why the U.S. is protecting the shipping lanes for other countries “for zero compensation.”

“All of these countries should be protecting their own ships on what has always been a dangerous journey.” He said the U.S. doesn’t “even need to be there” because it produces much of its own energy needs.

Trump ally Sen. Lindsey Graham, R-S.C., tweeted back that America’s allies in the Strait of Hormuz should do more but emphasized that, “safe navigation of sea lanes — vital to a world economy — is always in America’s national security interest.”

“Protecting sea lanes is best achieved by partnerships where all the stakeholders contribute and sacrifice for peaceful navigation of the seas,” Graham said. “Peace and economic prosperity are best achieved when bad actors are dealt with through international coalitions.”

Brian Hook, the U.S. special envoy for Iran, said one option could be to “enhance” an existing multinational maritime force of about 30 countries that currently fights drug and arms smuggling in the region.

Alternatively, he said allied nations with commercial interests in the oil-rich region could launch an all-new maritime security initiative.

Another option could be military ships patrolling the Gulf waters and equipped with surveillance equipment to keep watch on Iran.

The narrow Strait of Hormuz, which lies between Iran and Oman and opens to the Persian Gulf, is paramount for Asian oil importers. An estimated 18 million to 20 million barrels of oil — much of it crude — pass through the strait every day.

Today, any conflict that threatens tankers would badly disrupt crude supplies for energy-hungry countries like China, Japan, South Korea, Singapore and Indonesia, which are among the top five importers of Arabian oil.

Pompeo, meanwhile, emphasized the importance of maritime security minutes after Trump’s tweet. He and Saudi leaders, he said, discussed the need “to promote maritime security in the Strait of Hormuz” and added that “freedom of navigation is paramount.”

The Associated Press contributed to this report.