"'We will find the right way and at the right time to respond to this", he warned.
The existence of an understanding was confirmed by the U.S. Treasury Secretary who told reporters on Tuesday that "we have had conversations with various parties. that would be willing to increase oil supply".
Mr Falih said Saudi Arabia is not targeting a specific price for oil, discounting a May 4 report in The Wall Street Journal that Riyadh wants to oil to hit at least Dollars 80 a barrel this year.
The U.S. advised countries that want to avoid sanctions on their financial institutions to reduce their volume of crude purchases from Iran during a 180-day wind-down period.
Saudi Arabia has already promised to "mitigate" the impact of any potential supply shortages, in conjunction with other suppliers and consumer countries, in a statement released immediately after the sanctions decision.
CNN host Wolf Blitzer asked, "What will Saudi Arabia do?"
While Gulf petro-states stand to benefit from a rise in prices, the USA move could mean new fissures in the region.
Trump said on Tuesday that the United States was reimposing the "highest level of economic sanctions" on Iran, but he did not provide details.
Rouhani: Plans in place for Trump move on nuclear deal
But Trump and Netanyahu find themselves largely alone in an worldwide arena that is largely favorable of the nuclear agreement. Trump also objects to the accord's sunset clause, which allows Iran to resume part of its nuclear program after 2025.
Trump's claim that his withdrawal decision from the Iran deal will strengthen his hand in negotiating a better Iran deal is yet to be proven.
Qatar, alienated by a Saudi-led boycott, said priority must be given to non-proliferation and preventing a nuclear arms race. Worldwide agencies responsible for inspecting compliance have said that Iran was in full cooperation with the agreement's terms.
But the US sanctions on Iran, assuming they are effective, mark the end of the current output agreement.
Trump said his decision to leave the JCPOA was created to counter that possibility. The JCPOA is in America's interest - it has significantly rolled back Iran's nuclear program.
But Saudi Arabia has enough oil production capacity - now at 12 million barrels per day (bpd) - to maintain oil market stability, the source added. It violates United Nations resolutions with regards to ballistic missiles.
A ballistic missile launched by pro-Iranian Yemeni Houthi rebels was intercepted on its way to the capital Riyadh, Saudi media, including the website of Arab News, reported on Wednesday.
Even without disruption to Iran's crude flows, the balance between supply and demand in the oil market has been tightening steadily, especially in Asia, and as top exporter Saudi Arabia and No.1 producer Russian Federation have led efforts since 2017 to withhold oil supplies to prop up prices.