The unity that Republicans briefly enjoyed by sending an open letter to Iran in an attempt to disrupt a nuclear deal has cracked, as several conservative congressmen and media outlets described the letter as a folly.

Senator Bob Corker, one of the few Republicans in the chamber who did not sign the letter, told the Daily Beast that he “immediately knew that it was not something that, for me anyway, in my particular role, was going to be constructive”.

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“I didn’t think it was going to further our efforts to get to a place where Congress would play the appropriate role that it should on Iran,” he said.

Senator Jeff Flake and hawkish representative Peter King also called the wisdom of the letter into question. King told reporters on Tuesday he thought the letter set a poor precedent: “I don’t trust the president on this, quite frankly, though I don’t know if I’d go public with it to a foreign government.”

Related: Republican Iran letter not the action of ‘reasonable people’, says Clinton

Flake said the letter was “not appropriate or productive”, and that the matter of Iran’s nuclear capabilities is “too important to divide us among partisan lines”.

Flake’s comments echoed those of Democrats who continued to excoriate Republicans over the letter. Senator Debbie Stabenow took to the chamber floor to quote former senator Arthur Vandenberg, a Republican during the second world war who she said “loathed” president Franklin D Roosevelt.

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“‘Politics stops at the water’s edge,’” Stabenow quoted Vandenberg. “I can only imagine what senator Vandenberg would say if he were alive today,” she said, about Republicans who had “decided to throw away 70 years of wisdom and stand on the side of the ayatollahs”.

Florida Democrat Bill Nelson also urged Republicans to keep perspective: “We can disagree about the specifics but we still have to honor the institution of the presidency, and when it becomes matters of war and peace then we’ve got to unify.”

The letter to Iran, designed to undermine nuclear program negotiations between the Obama administration, Tehran and European powers, was signed by 47 of 54 Republican senators. The issue, underscored by a speech to Congress by Israeli prime minister Binyamin Netanyahu – at Republicans’ invitation – that railed against the deal, allowed Republicans to briefly unite on a policy point. The party has otherwise been riven by conservative and libertarian factions who disagree about issues such immigration, the economy and foreign intervention.

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But the condescending tone of the letter, which suggested that Iranians do not understand the American political process, provoked harsh words from both the Obama administration and even Iran’s foreign minister.

The minister, Mohammad Javad Zarif, called the letter a “propaganda ploy” and derided Republicans for failing to understand international and US law. Harvard law professor Jack Goldsmith notes that Zarif has a valid point : the letter incorrectly states that the Senate has the power to ratify treaties, which it does not – a fact stated even on the Senate’s own website .

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President Obama said that the letter put Republican senators in an “unusual coalition”, saying: “It’s somewhat ironic to see some members of Congress wanting to make common cause with the hardliners in Iran.” Vice-president Joe Biden said the the letter was “beneath the dignity of the institution I revere”.

Conservative media sources such as the Wall Street Journal and Fox News, both owned by Rupert Murdoch, also shied away from the letter. The Journal’s editors published an editorial calling the letter a “distraction ”. Fox host Megyn Kelly asked Senator Tom Cotton, the letter’s author: “What’s the point in writing to the Iranian mullahs?”

“They dismissed it already,” she pressed, “you’ve offended the Obama administration and you may have offended some of the Democrats who would have come over with the Republicans depending on what happens with this deal, to have a stronger say in the Senate.”

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In Iran, even ayatollah Mahmoud Shahroudi suggested that negotiations deserve a chance to succeed, according to state-owned the Islamic Republic News Agency. Iranian officials “are seeking to advance national interests and we support them”, Shahroudi said in a statement.

Shahroudi’s support reiterates Zarif’s position, which finds Republican intransigence “unfortunate” but is still “certain that there are measures to achieve such a deal”.

Cotton and other hawkish Republican senators have defended the letter , saying that their intention is primarily to prevent Iran from attaining the ability to create a nuclear weapon.

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