Some hard-liners close to the inner circle of Iran's supreme leader, Ayatollah Ali Khamenei, also have indicated their desire to tear up the agreement.
The act sanctions Iran for its support of terrorist organizations but also grants the President the authority to levy additional sanctions on Tehran if it is found to be violating the terms of the nuclear deal.
Last week, the US House of Representatives reviewed the sanctions and suggested an extension for another 10 years. "The latest is extension of sanctions for 10 years, that if it happens, would surely be against JCPOA, and the Islamic Republic would definitely react to it".
It eased economic sanctions on Iran in exchange for limits on Tehran's nuclear program.
The White House said the Obama administration would fulfill its obligations under the deal and there would not be any changes to the enforcement of it.
"The current U.S. government has breached the nuclear deal on many occasions".
Khamenei's remarks came one day after Iranian lawmakers in a statement deplored the vote, according to the semi-official Fars news agency.
"I imagine when the USA president practically takes the country's leadership, he will take actions on the basis of the realities as the nuclear deal is not an issue between the two countries to allow the other side to defy its undertakings, and we believe that there will be no problem", Salehi of the Atomic Energy Organization of Iran (AEOI) was quoted as saying.
Salehi added: "It is an global issue and we think that we will not face so many problems". They also blamed Obama for not having imposed or implemented "additional measures" against Tehran that could result in complicating the incoming USA administration's ability to develop its own policy.
"Any actions that are taken, if there are any, are the kinds of actions that have been in the pipeline for quite some time and are entirely consistent with the United States upholding our end of an agreement that has prevented Iran from developing their nuclear weapon capability", he added.
U.S. Secretary of State John Kerry took a lead role in negotiating the agreement and called it "the good deal we had sought".
During a speech to a pro-Israel group in March, Trump said as president, he would seek to end "the disastrous deal with Iran".