In a written statement, Trump said the following: "Today, I am waiving the application of certain nuclear sanctions, but only in order to secure our European allies' agreement to fix the terrible flaws of the Iran nuclear deal".
Two of those arrested died in prison in the aftermath of the protests, in what officials said were suicides. It also said Iran would not allow the deal to be linked to other issues, following the president's suggestion the deal be tied to Iran limiting its long-range ballistic missile program.
"Either fix the deal's disastrous flaws, or the United States will withdraw", he added.
The Iranian Ministry of Foreign Affairs on Saturday criticised the fresh sanctions imposed by the US by calling them illegal and hostile, and warned that they would receive a serious reaction by the Islamic republic.
It is the responsibility of all parties concerned and the common wish of the international community to continue to implement the pact, Xinhua news agency quoted Wang as saying during the call. The enormous financial windfall the Iranian regime received because of the deal - access to more than $100 billion, including $1.8 billion in cash - has not been used to better the lives of the Iranian people.
Under the deal, Iran agreed to curb its nuclear programme, in exchange for lifting of most sanctions. You have a regime that supports terrorism and is prone to cracking down on their own people and involving themselves in belligerent wars against their neighbors.
This would not entail negotiations with Iran, the official said, but rather would be the result of talks between the United States and its European allies. Bob Corker (R-TN) and Ben Cardin (D-MD) have been working with White House National Security Adviser H.R. McMaster on an agreement that would keep the Iran deal intact.
Iran has said its nuclear program is strictly for peaceful uses.
In October, he refused to recertify for Congress that Iran was complying, accusing it of "not living up to the spirit" of the agreement.
Under U.S. law, the sanctions can be waived for a maximum of 120 days, meaning the U.S. government must review the situation every four months.
The 2015 deal, known as the Joint Comprehensive Plan of Action, was signed by the U.S. under the previous administration of president Barack Obama as well as Iran, China, Russia, Britain, France and Germany.