Sen. Chris Murphy (D-Conn.), a supporter of diplomacy with Iran, said the framework agreement to curb Tehran's nuclear program that was announced last week was "a pretty remarkable deal" that takes unprecedented steps to roll back Iran's nuclear capabilities.

Among the key points in the framework are international inspections of Iran's nuclear supply chain and Tehran's agreement not to enrich uranium above a certain level for at least 15 years. In an interview on NBC's "Meet the Press," Murphy said the inspections will be able to uncover any covert programs that may exist outside of known research facilities.

"It's true that this deal doesn't turn Iran from a bad guy into a good guy," Murphy said in response. "But it's a little bit of rewriting of history to suggest these negotiations were about all of the other nefarious activities of Iran in the region. These negotiations were about ending their nuclear program, such that we can start to lift up the moderate elements ...[and] talk about all these other issues."

Murphy also noted that other sanctions — including over Iran's ballistic missile program, the country's support for terrorism and record on human rights — remain. Those are not tied to Iran's cooperation with the nuclear agreement, and Congress and the president reserve the right to increase those if Iran undermines stability in the Middle East, he said.

"You take this issue [the nuclear program] off the table and you empower people like Rouhani and Zarif, who may see a different path for Iran — less as an irritant, more as a member of the global community," Murphy said, referring to the Iranian president and foreign minister. "And you may see a pathway to solving some of these other problems, and you can do it potentially without new rounds of traditional sanctions."

Energy Secretary Ernest Moniz, a key member of the U.S. negotiating team, echoed Murphy’s comments. He rejected Netanyahu’s accusations and said the agreement would set up a long-term process that will not “go away in a few years.”

The New York Times reported apparent differences in accounts about the deal in a fact sheet released by the United States and a statement released by Iranian Foreign Minister Mohammad Javad Zarif and European Union foreign policy chief Federica Mogherini. When asked about the Times report on CBS’s “Face the Nation,” Moniz said the two accounts were mostly consistent and emphasize different parts of the deal.