"We have to make Americans understand that they cannot talk to the great Iranian nation with the language of pressure and sanctions," Rouhani said in televised remarks. He spoke to a conference of economists, who he said were at the "forefront of the resistance" against the United States.
"What the Americans are doing today is putting pressure merely on the people," he said, according to a transcript of the remarks posted on the president's website.
US Secretary of State Mike Pompeo and other Administration officials have described the penalties as the "toughest sanctions ever placed" on Iran.
While the sheer number of people and entities sanctioned is larger than ever, many Middle East experts believe they will be less effective than the UN sanctions in place before the deal. That is because virtually every country in the world was behind the previous sanctions, while all but a handful of nations oppose their reimposition.
The most significant of the new measures is a prohibition against oil and gas sales, which provide the Iranian Government with 80 per cent of its total revenue.
The blacklisted companies include 50 Iranian banks, an Iranian airline and dozens of its planes, as well as officials and vessels in Iran's shipping and energy sectors.
US President Donald Trump withdrew from the 2015 nuclear deal in May and gave nations and businesses 180 days to wind down their oil purchases to "zero." The Administration has granted waivers to eight countries that have reduced their oil purchases from Iran but not stopped them entirely.
The countries allowed to keep buying oil from Iran temporarily under the sanctions include China's two biggest oil customers, China and India, Pompeo announced. Also granted waivers were Italy, Greece, Japan, South Korea, Turkey and Taiwan.
In addition, Pompeo said the United States has granted waivers to continue three nonproliferation projects that provide oversight on Iran's nuclear programme.
The only one he identified was in Bushehr, where Russia is building a second unit at an existing nuclear power plant.
Since May, Europeans have said repeatedly that they want to preserve the nuclear deal and have focused their diplomatic efforts on keeping trade alive with Iran however possible.
In August, the European Commission revamped its Blocking Statute, a 1995 law designed to help European companies and banks recover damages arising from US sanctions on third parties. The legislation also implies that European courts could nullify US decisions regarding sanctions.
However, many European companies with a US presence remain cautious about those European tools, whose effectiveness has yet to be tested.