The US President said documents "conclusively" showing the Iranian regime was pursuing nuclear weapons informed his decision to pull out of the landmark nuclear agreement.
Lord Lamont said that Mr Trump's actions were motivated by rivalry with previous president Barack Obama, under whom the 2015 nuclear deal was signed. Tehran says the move defies a UN Security Council resolution.
Aside from restrictions on oil imports, the administration added more than 700 names - including individuals, entities, vessels and aircraft linked to the energy and financial sectors and other segments of Iran's economy - to the U.S. list of sanctioned entities.
"We are in a situation of economic war, confronting a bullying power. I don't think that in the history of America, someone has entered the White House who is so against law and worldwide conventions", he added.
The ministry's spokesman, Baharam Ghasemi said the sanctions would backfire and work against the U.S. and that "many countries from Europe to Russian Federation and China have opposed the sanctions".
But the country's Supreme Leader, Ayatollah Ali Khamenei, is not so sure.
"There is no need for mediation. We must resist and win". "I don't support this policy, but if you are going down this path, it's a way to lessen the risk of economic blowback in America".
While Iran's crude exports could fall to little more than 1 million barrels per day (bpd) in November, traders and analysts say that figure could rise again from December as importers use their waivers to order crude from Iran.More news: Hopes for Brexit deal grow with 'major step' over border issue
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The Belgium-based SWIFT financial messaging service said on Monday it is suspending some unspecified Iranian banks' access to its messaging system in the interest of the stability and integrity of the global financial system.
The US imposed a first round of sanctions on Iran in August and Monday marked the second round of sanctions that went into effect.
Rouhani's plan since his election in 2013 was to boost the economy by rebuilding ties with the world and attracting billions of dollars in foreign investment - a strategy that now looks in tatters. We told them that India is an energy reliant country and an abrupt reduction of oil imports from Iran will affect our economy.
One notable exemption was Iraq. "We continue to believe that the Iran nuclear deal makes the world a safer place and our position remains that as long as Iran continues to meet its obligations under the deal by respecting strict limits on its nuclear activity, we will be committed to it too", Prime Minister Theresa May's spokesman said.
One country that USA sanctions officials could watch closely is the United Arab Emirates, which occupies a patch of geography vital to Iran's ability to move oil legally or illegally out of the Persian Gulf. Right now we have a history last time around of India, Turkey and China continuing to buy even with sanctions.
"Any financial institution, company, or individual who evades our sanctions risks losing access to the U.S. financial system and the ability to do business with the United States or USA companies", Mnuchin said.
Pompeo promised that the United States will be "relentless" in pressuring Iran as he announced the temporary exemption list.
Since then, Iran has provided arms and financial support to militant groups active in the Middle East and further afield.