North Korea is under USA and United Nations sanctions over its nuclear weapons programme.
Tuesday's sanctions target Iran's purchases of US dollars, metals trading, coal, industrial software and the auto sector.
In November, a second batch of potentially more damaging sanctions will be reinstated on Iran's port operators, and the energy, shipping, and shipbuilding sectors.
"NEVER, EVER THREATEN THE UNITED STATES AGAIN OR YOU WILL SUFFER CONSEQUENCES THE LIKES OF WHICH FEW THROUGHOUT HISTORY HAVE EVER SUFFERED BEFORE", Trump wrote.
The high-level meeting follows the reimposition of sanctions on Iran by the us on Tuesday, which a White House statement said targeted the country's energy sector and foreign financial institutions doing business with the Central Bank of Iran.
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.
"The US withdrawal from JCPOA and re-imposition of its sanctions is a serious breach of its legal obligations under the United Nations Charter, which entails its global responsibility".
European countries, hoping to persuade Tehran to continue to respect the nuclear deal, have promised to try to lessen the blow of sanctions and to urge their firms not to pull out.
Donald Trump brought back the punishing sanctions after unilaterally pulling out of a landmark 2015 deal between Tehran and Western powers to halt Iran's nuclear ambitions.More news: Samsung Begins Mass Production of 4-Bit 4TB SSD for Consumers
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Among those that have suspended plans to invest in Iran are France's oil major Total, its big carmakers PSA and Renault, and their German rival Daimler.
"America has zigzagged constantly, so now no one trusts them", he said.
Turkey, however, said it would continue to buy natural gas from Iran.
North Korean Foreign Minister Ri Yong Ho met with his Iranian counterpart Mohammad Javad Zarif in Tehran on Tuesday, according to the Foreign Ministry's website.
USA 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.
Iran is a key supplier of natural gas and oil to Turkey, which is nearly 100-percent dependent on fuel imports.
U.S. Central Command head Gen. Joseph Votel said he believes that the exercise was meant to be a message to Washington over re-imposing economic sanctions on Iran.
"The financial and political war against the regime will continue and I anticipate Iran's predicament will only worsen", Dubowitz told the Washington Free Beacon.