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It follows the IAEA's announcement on Saturday that Iran had implemented the terms of the nuclear agreement, which would allow for trade between some western nations and Tehran to resume.

Americans held by Iran were released on the same day.

But US frontrunner Donald Trump questioned US gains from the deal and the prisoner exchange through deft calculations.

"They're getting seven people, so essentially they get $150bn plus seven, and we get four," Trump said.

Ben Carson, also a candidate for the Republican nomination for president, pledged to withdraw from the agreement on his first day if elected as the country's leader.

"The fact remains that President Obama's nuclear agreement with Iran is fatally flawed and gravely jeopardises the national security interests of the American people, our ally Israel and other peaceful nations in the Middle East and around the world," Carson said.

Former Republican governor of Florida and Republican candidate Jeb Bush called for new sanctions against the Islamic Republic.

"The bigger issue is that we've legitimised a regime that shows no interest in actually moving forward with the so-called community of nations," the brother of former US President George Bush said.

The US congress' house of representatives Speaker, Paul Ryan, also criticised the deal with Tehran.

"A bipartisan majority in the house voted to reject this deal in the first place, and we will continue to do everything possible to prevent a nuclear Iran," Ryan said.

In a surprising move, Democrat presidential hopeful Hilary Clinton - who was part of the previous Obama administration - also called for new sanctions.

"As president, my approach will be to distrust and verify [Iran's actions]," Clinton said in a statement.

"Iran is still violating UN security council resolutions with its ballistic missile program, which should be met with new sanctions designations and firm resolve," she added.

The deal with Iran may turn into a political flashpoint for the Obama administration in the US.

However, following three decades of hostility between Washington and Tehran the deal could well be the foreign policy achievement Obama is remembered for during his time as president.

The US and EU confirmed on Saturday that Iran has met all of its nuclear deal commitments and economic sanctions against the Islamic Republic can now be lifted.

For Iran this means an end to crippling western economic sanctions.

Access to its frozen assets of $100 billion will unleashing new opportunities for its battered economy amidst a major drop in oil prices.

In a display of intense diplomacy between the long-time enemies, Iran released US prisoners in the lead up to the lifting of the sanctions including Washington Post journalist Jason Rezaian, as part of a prisoner swap with the US.

Iran's President Hassan Rouhani rejoiced at the implementation of the deal with world powers, most notably its long-time enemy US, calling it a "glorious victory" for the "patient nation of Iran".

The Obama administration hailed the accomplishments of the nuclear talks and staunchly defended its deal with Tehran against much of the criticism it was getting from back home.

"The United States, our friends and allies in the Middle East and the entire world are safer because the threat of a nuclear weapon has been reduced," Secretary of State John Kerry told reporters in Vienna.