"Maintaining pressure on Iran through our existing sanctions is essential," four European foreign policy chiefs warned in a joint op-ed in the Washington Post.
"But introducing new hurdles at this critical stage of the negotiations, including through additional nuclear-related sanctions legislation on Iran, would jeopardize our efforts at a critical juncture."
EU foreign policy chief Federica Mogherini joined forces with British Foreign Secretary Philip Hammond and his French and German counterparts, Laurent Fabius and Frank-Walter Steinmeier, to urge Congress to give diplomacy "the best possible chance to succeed."
The ministers said the goal of the P5+1 group leading the negotiations with Iran was "a comprehensive solution that both recognizes the Iranian people's right to access peaceful nuclear energy and allows the international community to verify that Iran cannot obtain a nuclear weapon."
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But it was a complex and difficult task, so the ministers said "we extended the negotiating window until later this year."
As the clock ticks down, bilateral Iran-US talks will resume in Zurich on Friday and Saturday.
But draft legislation is already being drawn up in the Senate to slap new sanctions on Iran, even though President Barack Obama has said he will veto any such bill.
"Rather than strengthening our negotiating position, new sanctions legislation at this point would set us back," the Europeans wrote, adding it might also "fracture" the coalition maintaining the current sanctions regime.
"For the first time, however, we may have a real chance to resolve one of the world's long-standing security threats - and the chance to do it peacefully... We have a historic opportunity that might not come again.