Hakim said the policy of threatening and putting the countries under economic siege is "wrong" and "unfair", ISNA reported on Saturday.
"Together, we can help bring about the peace and prosperity in Iran that the whole world wants to see".
He added unilateral actions which run contrary to the United Nations regulations are condemnable.
The decision came after U.S. President Donald Trump withdrew from a landmark 2015 nuclear deal between Iran and world powers.
The administration is poised to impose a second wave of sanctions in November.
Britain remained open to talks with the USA on how to address concerns about Iran.
The U.S. sanctions that began last week prohibit any transactions with Iran involving dollars, gold, precious metals, aluminum, steel, commercial passenger aircraft, shipping and Iranian seaports.
The first hearing session in the case will be held on August 27.
He added, "America is turning up the pressure and we want the United Kingdom by our side".
"We are asking global Britain to use its considerable diplomatic power and influence and join us as we lead a concerted global effort towards a genuinely comprehensive agreement".
Last week the European Union's executive Commission introduced a "blocking statute" to protect European businesses from the impact of the sanctions.
The U.S. administration blames Iran for fomenting instability in the Middle East and encouraging terrorism.
Accusing Iran of "squandering its money on proxy wars and malign activities overseas", US Ambassador Woody Johnson's op-ed in the Sunday Telegraph asked the UK to "use its considerable diplomatic power and influence" to join the US "as a united front" in its effort to secure "a genuinely comprehensive agreement" on Iran ending its nuclear program. "It is time to move on from the flawed 2015 deal", he said.
Britain's May might face a party leadership challenge later in the year, possibly from Boris Johnson, the former foreign minister who says she should be more like Trump.
While Washington was busy exiting the Iran nuclear deal in early May, Rabat had its own issues with the Islamic Republic. Of all the G-7 leaders at the bruising summit, she largely side-stepped the public skirmishing.
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