WASHINGTON — Over four-fifths of the US Senate sent a letter Tuesday to President Barack Obama in which they insisted that Iran give up its capacity to break out to a nuclear weapon and warned of the circumvention of existing sanctions under the interim deal with Tehran.

A bipartisan majority of 83 senators signed on to the letter, which was circulated in recent weeks by Senate Foreign Relations Committee Chairman Robert Menendez (D-NJ) and Sens. Lindsey Graham (R-SC), Charles Schumer (D-NY), Mark Kirk (R-IL), Christopher Coons (D-DE) and Kelly Ayotte (R-NH).

In the letter, the senators emphasized their support for the ongoing negotiations between the six world powers and Iran, but insisted that 20 years’ worth of Congressional commitment to sanctions against Iran were what brought the Iranians to the negotiating table in the first place.

Those negotiations resumed Tuesday morning with a meeting in Geneva between EU policy chief Catherine Ashton and Iranian Foreign Minister Mohammad Javad Zarif. The new round of talks is the second in a planned series of meetings this year that aims to transform November’s interim deal between Iran and the world powers — the five permanent members of the UN Security Council plus Germany – into a lasting accord by July.

The letter was a victory for AIPAC, whose activists had pushed for it during a legislative action day two weeks ago. The organization said in a statement Tuesday that it “applauds this overwhelming demonstration by the US Senate of its determination to prevent Iran from achieving nuclear weapons capability.”

In the letter, senators warned that in order to achieve a successful diplomatic outcome, Washington must “couple our willingness to negotiate with a united and unmistakable message to the Iranian regime.”

The letter addressed recent reports that even under the limited sanctions relief offered by the interim agreement, Iran’s economy was improving beyond predictions made by US administration figures.

“Iran must not be allowed during these negotiations to circumvent sanctions,” the senators wrote. “We view this period as one fraught with the danger of companies and countries looking to improve their commercial position in Tehran, especially given recent reports of rising purchases of Iranian oil. Iran cannot be allowed to be open for business.”

The senators emphasized that “Congress has a continuing role to play to improve the prospects for success in the talks with Iran” and promised that as negotiations proceed, they would “outline our views about the essential goals of a final agreement with Iran, continue oversight of the interim agreement and the existing sanctions regime, and signal the consequences that will follow if Iran rejects an agreement that brings to an end its nuclear weapons ambitions.”

The letter laid out core principles that the senators believe should delineate American positions in final status talks, including denying Iran any “right to enrichment under the Nuclear Proliferation Treaty” and calling on Iran to dismantle its entire alleged nuclear weapons program. The letter specified that the latter included denying Iran the ability to create a bomb using either enriched uranium or plutonium, which could be produced by the heavy water plant in Arak. The senators specifically called for the regime to give up the Arak reactor and to “fully explain the questionable activities in which it engaged at Parchin and other facilities.” The military base at Parchin is suspected of being a site for testing delivery systems for nuclear weapons.

The office of Menendez, the Senate Foreign Relations Committee chairman, emphasized the line in the letter that said that “most importantly, Iran must clearly understand the consequences of failing to reach an acceptable final agreement. We must signal unequivocally to Iran that rejecting negotiations and continuing its nuclear weapon program will lead to much more dramatic sanctions, including further limitations on Iran’s exports of crude oil and petroleum products.”

Although the administration has pushed Senate Democrats not to sign on to the Nuclear Weapons Free Iran Act, which would delineate the sanctions to be imposed should Iran back away from talks, a number of senators who have not co-sponsored the bill signed on to Tuesday’s letter. Menendez, together with Senator Mark Kirk (R-IL) are the original sponsors of the bill, which has 67 other Senate co-sponsors.