However, he did call for stringent measures to keep the agreement alive. He also waived off nuclear-related sanctions on Iran -- a requirement to keep the deal alive.
Iran, however, rejected any modification to its nuclear deal.
Iran "will not accept any amendments in this agreement, be it now or in the future, and it will not allow any other issues to be linked to the JCPOA," the foreign ministry said in a statement.
Trump asked the European partners to work with the United States in order to "fix the deal's disastrous flaws," in the absence of which the United States will withdraw from the deal, Trump threatened.
Trump demanded restrictions on Iran's missile programme and called for permanent control on Iran's nuclear plants.
Iran, on the other hand, clarified that the deal remains renegotiated.
"JCPOA is not renegotiable: rather than repeating tired rhetoric, US must bring itself into full compliance -- just like Iran," Iran's foreign minister, Mohammad Javad Zarif tweeted immediately after Trump's speech.
Iran's foreign ministry condemned fresh sanctions imposed by the US on 14 individuals, including judiciary chief Ayatollah Sadegh Larijani, over human rights issues.
The ministry also criticised US sanctions on Iran's missile programme and described restrictions on Larijani to have "crossed all red lines of conduct in the international community."
The official statement from Iran's foreign ministry stated that "the government of the United States will bear responsibility for all the consequences of this hostile move".
Iran argued that the continued US sanctions on non-nuclear areas such as human rights and missile testing have effectively barred Iran from gaining many of the financial benefits expected from the deal.
Zarif condemned Trump's aggressive stance on the deal and Iran describing the White House to also have violated the commitment to "refrain from any policy specifically intended to directly and adversely affect the normalisation of trade and economic relations with Iran" in the accord.