His comments come a day after Russian Energy Minister Alexander Novak said Moscow would continue to buy Iranian oil, even after USA sanctions go back into place on Monday.
Mr Rouhani, meanwhile, pledged to government officials in comments aired on state television that Iran would overcome the sanctions. Other parties to the deal, including Britain, France, Germany, China and Russian Federation, have said they will not leave.
Iran's already-anemic economy is likely to suffer more under the fresh U.S. embargo, though politicians and protesters struck a defiant tone.
Trump said the deal, approved by predecessor Barack Obama, was weak and flawed in Iran's favour.
Wallace then asked Pompeo if it's true that the Trump administration will be giving exemptions to China and India, and if so, does the White House "have a firm commitment that within six months, they will stop all oil purchases?"
Rouhani pledged to government officials in his remarks that Iran would overcome the U.S. embargo.
The new sanctions will particularly hurt Iran's oil industry, a crucial source of money for its anaemic economy.
Meanwhile, Iran's supreme leader Ayatollah Ali Khamenei said on Saturday that President Donald Trump has "disgraced" U.S. prestige and would be the ultimate loser from renewing sanctions on the Islamic republic. The US withdrawal from the nuclear deal has already had a huge effect, including the devaluing of the Iranian rial and oil exports falling by about a million barrels a day.
In fact, Iran had regained its position of the third largest exporter of crude oil to India and had been offering attractive terms to oil companies like Indian Oil Corp (IOC) and Mangalore Refinery and Petrochemicals (MRPL) with a 90-day credit period and full insurance cover for ships.
He further stepped up the rhetoric, comparing Iran's situation in the 1980s war against Iraqi dictator Saddam Hussein with the current one and President Donald Trump's move to reinstate U.S. sanctions.
They will directly affect companies from third countries doing business with Iran.
"We are in the war situation", Rouhani said.
Iran is already in the grip of an economic crisis. "The new sanctions might prove to be costly if the Kingdom of Saudi Arabia, with spare production capacity, is unable or unwilling to put more oil in the market". "But America's plots and its plans for sanctions will be defeated through continued resistance", he said.
However, analysts doubt this will materially lessen the impact of sanctions on Iran.
Before travelling to a campaign rally for the USA mid-term elections, President Donald Trump said Iran was already struggling under his administration's policies. "This is a substantial drop", she said, adding that the ultimate goal was to deprive the regime of revenue it gets from oil.