"Iran will offer its oil in the stock market, and the private sector can transparently buy and sell the crude through this market", Jahangiri added.
Trump was not specific on whether the additional 2 million barrels was a per-day figure - but worldwide daily demand is nearing 100 million bpd.
Oil prices rose on Friday on worries that USA sanctions against Iran would take away significant volumes of crude oil from world markets while oil demand worldwide increases.
"Yes, of course. That's what we're doing".
"We will not hesitate to take action when we see sanctionable activity", said Brian Hook, the department's Policy Planning Director and the former lead negotiator for the USA who met with European allies for months to reach a side agreement that kept the U.S.in the Iran nuclear deal but addressed Trump's concerns with it.
In a tweet on Saturday, Trump said the extra Saudi oil would help offset a decline in supply from Iran, after the United States pulled out of the Iran nuclear deal in May and moved to reimpose oil sanctions.
On Tuesday a senior State Department official described tightening the noose on Tehran as "one of our top national security priorities".
European countries have been attempting to negotiate exemptions for their firms, but the official confirmed that US President Donald Trump intends to stick to his deadline.
The Organization of the Petroleum Exporting Countries agreed with Russian Federation and other oil-producing allies on June 23 to raise output from July, with Saudi Arabia pledging a "measurable" supply boost, but giving no specific numbers.
The Trump administration's ban on Iranian oil threatens to prompt a crude shortage, analysts say, that could hit American taxpayers at the gas pump just as they expect some relief in gas prices after the summer.
"They're begging the Saudis to raise their output so that if Iran's quota decreases nothing will happen to the markets", said Jahangiri.
Some 50 global companies had announced their intention to leave the Iranian market, particularly in energy and financial sectors, as the United States moved to reimpose the sanctions against Iran, Hook said.
An oil tanker is being loaded at Saudi Aramco's Ras Tanura oil refinery and oil terminal in Saudi Arabia May 21, 2018.
"Any increase in the production by any member country beyond commitments stipulated in OPEC's decisions ... would constitute a breach of the agreement", Zanganeh wrote in his letter, seen by Reuters and also reported by state media on Sunday.