"Today, I am waiving the application of certain nuclear sanctions, but only in order to secure our European allies' agreement to fix the awful flaws of the Iran nuclear deal", he said in the statement.
The U.N. nuclear watchdog agency has repeatedly found Iran is complying with those obligations. Nevertheless, many other restrictions, for instance over Iranian ballistic missiles, remained in place.
Russian Federation - one of the parties to the Iran pact alongside the United States, China, France, Britain, Germany and the European Union - called Trump's comments "extremely negative". Under the current deal they are set to expire in 2025.
On Friday, announcing his decision to waive the application of certain sanctions related to oil sales and Iran's banking system, he said he was only making the move to secure European allies' agreement to fix the deal's "flaws".
In reply, Zarif took to Twitter on Friday to condemn Trump's reluctant announcement on the nuclear sanctions waiver, saying, "Trump's policy & today's announcement amount to desperate attempts to undermine a solid multilateral agreement, maliciously violating its paras 26, 28 & 29".
Report says in the final agreement, the West promises to relieve sanctions on Tehran in exchange for a halt in Iran's efforts to develop a nuclear weapon.
But Trump, who must meet regular deadlines to endorse the deal every 90 days and approve sanctions waivers every 120 and 180 days, has railed against the agreement.
"If at any time I judge that such an agreement is not within reach, I will withdraw from the deal immediately", he added.
But Trump argues that his predecessor Barack Obama gave away too much to Iran in sanctions relief, without forcing the Islamic republic to end its ballistic missile program and support for militant groups.
U.S. officials expect the White House to issue a statement later Friday to confirm that Trump has grudgingly signed the sanction waivers once again before they start to expire this weekend - though he is also expected to impose new sanctions on Tehran over non-nuclear issues.
"This is a last chance", Trump said in a statement.
He was among those calling for a crackdown following a recent spate of anti-government protests across Iran.
Washington policy hawks hailed Trump's decision, which they said would concentrate minds in Europe, where leaders have urged the United States president not to sabotage a deal they see as a landmark diplomatic success.
Trump's declaration puts great pressure on Britain, France and Germany, the European signatories to nuclear pact with Iran.