U.S. President Donald Trump opened an anti-terrorism center in Saudi Arabia during his tour in the region, and accused Iran of being a key source of funding and support for militant groups in the Middle East.
Trump added that he had detected, too, "a growing realisation among your Arab neighbours that they have common cause with you in the threat posed by Iran".
He also demanded that Iran cease its support of "terrorists and militias". He added that, "we do not agree with isolation of Iran on the basis of a leader democratically elected by the people of Iran".
Iran shot back on Monday morning, as the foreign ministry accused the USA of selling arms to "dangerous terrorists" in the Middle East and of spreading "Iranophobia" aimed at encouraging Arab states to buy weapons.
The Republican congress and the Trump Presidency in the United States will not be almost as willing to cut deals with the Iran - already negotiating large arms sales to Iran's main political opponent Saudi Arabia.
Iran is one of the lead oil producers among members of the Organization of Petroleum Exporting Countries.
In a jibe at the multibillion-dollar arms deals signed between Mr Trump and the Saudi government at the weekend, he said: "You can't solve terrorism just by giving your people's money to a superpower".More news: Trio of 65s lead Colonial; 2-time champs 2 back, Spieth even
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Mr Rouhani stressed that it was Syrians, Iraqis, Iranians and members of Lebanon's Hezbollah movement who had been fighting terrorists in the Middle East in recent years, and accused the USA and its allies of funding terrorists.
Rouhani called relations with the United States "a curvy road", saying he hoped the Trump administration will "settle down" enough for his nation to better understand it. But Trump was unmoved by the Iran election results, calling on other nations to isolate the Persian Gulf nation entirely.
Trump delivered this remarkable farrago of lies and half-truths two days after Iran, the only Middle Eastern state apart from Israel and Turkey to hold relatively free elections, re-elected President Hassan Rouhani, who has worked hard to reduce the influence of his hard-line opponents. He has bought into a partisan Arab narrative whose theme is an inevitable (and ultimately military) conflict between Iran and the Arab world, and has all but promised that the United States would fight on the Arab side in that putative war.
He made veiled criticisms at security agencies that control large swathes of the Iranian economy and have sought to block his efforts to privatise and attract foreign investment.
Rouhani also told the news conference that he would continue Iran's ballistic missile programme.
Trump's visit to Israel was initially presented as an attempt to make a breakthrough in the moribund peace process between Israelis and Palestinians, but any talk of a deal has been overshadowed by his focus on Iran.
Yet Trump has yet to bring about the kind of change to America's Iran policy that he promised as a candidate, when he declared that Obama's nuclear agreement was "the worst deal ever negotiated".