Iranian parliament speaker Mohammad Bagher Ghalibaf said on Sunday that Tehran will not allow the reopening of the Strait of Hormuz until all of its conditions have been met.

"Over the past seven months, we have shown that we are not helpless in the face of aggression," Ghaliaf said in a statement published by the semi-official Fars News Agency.

"We must both fight and negotiate," said Ghalibaf, who led the Iranian negotiating delegation to Islamabad in April.

"Our messages have been conveyed and our conditions have been clearly explained to the other side through mediators, and the enemy knows very well that the path of deception and one-sided imposition is closed," Ghalibaf continued.

"Until these conditions are met, the legitimate rights of the Iranian people are recognized and the Americans fulfill their commitments, there will be no opening for a return to the previous conditions for negotiations or for the Strait of Hormuz to be opened," he said.

"Today, the old American order in West Asia has collapsed, and it is the Islamic countries of the region that must implement a new order," Ghalibaf added.

The State Department posted a security alert on Saturday evening advising Americans currently in the Middle East to "exercise heightened vigilance" and "be aware of potential flight cancellations, airspace closures, and travel disruptions."

"Iranian-supported Houthis have engaged in hostilities against Saudi Arabia, including civilian airports. This military conflict has the potential to escalate rapidly," the post said.

The alert also advised Americans outside the Middle East to "seriously reconsider travel to and through the region."

-ABC News' Lauren Minore

Iranian National Security Council Secretary General Mohsen Rezaei said in an interview with Al Jazeera on Saturday that Tehran wants an end to the war between Saudi Arabia and Yemen.

Talking about Iran’s nuclear program, Rezaei said the Islamic Republic remains "committed" to the former leader’s fatwa on its nuclear doctrine, which had prohibited the manufacture of a nuclear weapon. However, he said he does not know "what will happen in the future."

“We have not yet made a decision to withdraw from the NPT," said Rezaei, referring to the Treaty on the Non-Proliferation of Nuclear Weapons. He added that "this matter depends on Washington’s conduct."

He told Al Jazeera that Iran's conditions have been conveyed to the U.S. via mediators, Qatar and Pakistan. They include the lifting of a U.S. naval blockade and an end to the war on all fronts, as he said.

-ABC News' Somayeh Malekian

Saudi-led coalition spokesperson Major General Turki Al-Maliki said Saturday that Saudi air defenses intercepted a Houthi ballistic missile fired toward Riyadh.

In a statement posted on social media, al-Maliki said the Royal Saudi Air Defense Forces had "successfully intercepted and destroyed" a ballistic missile launched by the Houthis toward the Saudi capital at dawn.

The statement said the targeting of civilians and civilian infrastructure in Riyadh demonstrated what it described as the Houthis' "hostile and terrorist behavior."

Al-Maliki also said the Houthis attempted to target civilians and civilian sites in Yanbu, Baish, Taif and Farasan, but that all attacks were thwarted by Saudi air defense systems.

The statement did not mention any attack on Riyadh's international airport.

-ABC News' Jamie Dorrington

President Donald Trump is now saying that he is "open" to the "concept" of negotiating a deal with Iran.

"The failing Nation of Iran wants to make a deal, quickly and badly. I will determine whether or not the U.S.A. will choose to engage -- The concept of which we are open to,” Trump said on his social media platform on Monday.

This comes despite the president's recent comments casting doubt on Iran's trustworthiness and suggesting a deal wouldn't hold any value.

"I think an agreement with them isn't worth the paper it's written on," Trump told Fox News on Sept. 1. That day, he also posted: "I couldn't care less if they sign a worthless, to them, agreement."

On Sunday, Trump said he would only make a deal with Iran if it is the "right deal," but offered no other details about what this would look like.

-ABC News' Emily Chang