In comments carried by the Office of the President, Rouhani was said to have praised the two countries' "friendly and heartfelt relationship" and mutual support for each other, while warning that Washington should not be seen as trustworthy.
Iran's Labour Minister Ali Rabiei was impeached on Wednesday after months of mounting anger over the government's handling of an economic crisis which has deepened with the return of U.S. sanctions.
It will be followed in November by other measures affecting the oil and gas sector as well as the Central Bank.
Mohammed Javad Zarif's public advice came after the United States reimposed sanctions against Iran on Monday, as presaged by President Donald Trump's withdrawal from his predecessor Barack Obama's nuclear deal, formally known as the Joint Comprehensive Plan of Action (JCPOA).
US officials have said in recent weeks that they aim to reduce Iran's oil exports to zero as a means of pressuring Tehran to halt its nuclear and missile programmes and involvement in regional conflicts in Syria and Iraq. "There is no doubt about this", Khamenei was quoted as saying in comments that appeared only a day after the new us sanctions took effect.
Trump tweeted on Tuesday: "These are the most biting sanctions ever imposed, and in November they ratchet up to yet another level".
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One showed a cellphone video of a drone hovering over a residential street two blocks away and then crashing into a building. The Colombian foreign ministry denied involvement, saying the allegations were "absurd" and "lacked any foundation".
Rouhani hinted last month that Iran could block the Strait of Hormuz, a major oil shipping route, if the US attempted to stop the Islamic Republic's oil exports.
Mr Zarif added the idea of halting the exports of Iran's most valuable goods "simplistic and impossible" and will lead to "consequences".
Following Trump's announced United States departure from the deal in May, the White House has, through 17 rounds, sanctioned 38 Iran-related targets. Zarif told the state-owned IRAN daily, however, there are now no ongoing talks between the countries.
But that has proven hard, and European companies have quit Iran, arguing that they can not risk their US business. "We can't get drawn into a confrontation with America by falling into this war room trap and playing on a battlefield".
Russia, which remains a signatory of the 2015 deal along with the European Union and others, also slammed the US sanctions on Iran.
His visit to Iran is the first by a high-ranking DPRK delegation since August past year, when President of the Presidium of the Supreme People's Assembly Kim Yong Nam and vice foreign minister Choe Hui Chol spent several days in the country.
"If you stab someone with a knife and then you say you want talks, then the first thing you have to do is remove the knife", Rouhani said in a speech broadcast live on state television.