The minister did not identify a preferred short-term resolution.
Al-Faisal also said efforts supported by the US to rid the Middle East of nuclear weapons must apply to Israel.
Clinton is in the Persian Gulf to shore up support for new sanctions against Iran. She arrived in Riyadh on Monday night after visiting Qatar.
US officials travelling with Clinton said privately they were uncertain what al-Faisal meant, since the Saudi government has been explicit in its support of sanctions against Iran.
Earlier, in Qatar, Clinton said that Iran was heading towards a "military dictatorship" and warned it posed an international threat.
"We see the government of Iran, the supreme leader, the president, the parliament is being supplanted and Iran is moving toward a military dictatorship," Clinton told students at the Qatari branch of Carnegie-Mellon University.
The US is seeking to push Iran into curbing its nuclear ambitions, which it says are aimed at building a nuclear weapon.
Tehran has repeatedly stated that its nuclear programme is purely to meet the country's civilian energy needs.
Mohammad Marandi, a political analyst at the University of Tehran, dismissed Clinton's comments.
"If we give Hillary Clinton some more time she will be blaming Iran for global warming as well," he told Al Jazeera.
Watch Hillary Clinton's Middle East Town Hall meeting on Al Jazeera:
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"Obviously the statements that she has been making over the past couple of days are quite dishonest.
"The fact is the United States has to deal with Iran on a rational basis otherwise it will get itself nowhere."
The comments by Clinton marked a stepping up of pressure in favour of sanctions on Iran.
The US is hoping to use international pressure through the UN Security Council for a fourth round of sanctions on Iran.
Clinton said that those sanctions would expressly target the business interests of Iran's Revolutionary Guard.
But she added that Washington was not planning military action against Iran.
"We are planning to try to bring the world community together in applying pressure to Iran through sanctions adopted by the United Nations that will be particularly aimed at those enterprises controlled by the Revolutionary Guard, which we believe is, in effect, supplanting the government of Iran," she said.
Her comments came a day after she told delegates at the US-Islamic World Forum, also in Qatar, that Iran had left the world powers little choice but to impose harsh penalties against it over its nuclear programme.
Clinton told the forum, jointly organised by the Qatari foreign ministry and the US-based Brookings Institution, that "evidence is accumulating" that Iran is trying to build a nuclear weapon.
"Iran has consistently failed to live up to its responsibilities. It has refused to demonstrate to the international community that its nuclear programme is entirely peaceful," she said.
Mahmoud Ahmadinejad, Iran's president, said last week that his country's nuclear scientists had completed further enrichment of the first batch of its stockpile of uranium.
Tehran has said that it stepped up enrichment to produce fuel for a medical research reactor, but the US and its allies have said that the move signals a rejection of a UN-backed plan to swap Iran's low-enriched uranium for processed nuclear fuel.