The statement came as the Obama-era Iran nuclear deal approaches reauthorization next month. According to media reports, the EU3 powers - France, Germany and the United Kingdom - are working on a proposal to meet Trump's demands through new sanctions.
Trump's tone in this year's Nowruz message was a stark contrast from last year's, when he called the Iranian-American community "one of the most successful immigrant groups in our country's contemporary history".
"In particular, as we discuss Syria or as we discuss regional issues, the role of Iran comes on the table".
Without mentioning Trump by name, Iranian Foreign Minister Mohammad Javad Zarif appeared to tweet a response to the President's comments Tuesday. "I would expect today the discussion to be focused, first and foremost, on how to keep the full implementation of the nuclear deal, as it is being fully implemented now, also for the future, especially following a very good Joint Commission meeting we had on Friday altogether, with all the parties and with Iran".
The president said that the Treasury Department was issuing guidance "reaffirming America's support for the free flow of information to the citizens of Iran".
Iran agreed to curbs on its nuclear programme in exchange for the lifting of a number of sanctions as part of the deal.
Consider new sanctions on Iran
"We are determined to ensure that the Vienna accord is respected", French Foreign Minister Jean-Yves Le Drian told reporters on Monday before talks with his European Union counterparts, referring to the city where the 2015 deal was signed.
Britain, France and Germany have proposed fresh European Union sanctions on Iran over its ballistic missiles and its role in Syria's war, according to a confidential document, Reuters reported last week.
The confidential document cites "transfers of Iranian missiles and missile technology" to Syria and allies of Tehran, such as Houthi rebels in Yemen and Lebanon's Shi'ite Hezbollah.
"As alleged, Ali Sadr Hashemi Nejad created a network of front companies and foreign bank accounts to mask Iranian business dealings in Venezuela and evade US sanctions", Manhattan US Attorney Geoffrey Berman said in a statement.
"We were hopeful that after his recent visit to Tehran and negotiations with Iranian officials, he would understand the realities of the Islamic Republic's defense policies", Fars news agency quoted Iranian spokesman Bahram Qasemi as saying.
In the message marking the start of the spring New Year's festival, Trump said he was announcing that the Treasury Department would issue guidance "reaffirming America's support for the free flow of information to the citizens of Iran" and that the US would hold the regime accountable for cyber-attacks overseas.
Sex And The City star Cynthia Nixon running for NY governor
Republican leaders, meanwhile, have been coalescing behind Dutchess County Executive Marc Molinaro as a candidate, with state Sen. Miranda Hobbes for Governor? However, given his close connections to Nixon, de Blasio is unlikely to support Cuomo this time.