02:34 - Source: CNN
Hillary Clinton on Iran through the years
Washington CNN  — 

Hillary Clinton hailed the deal that the United States and other world powers struck with Iran on Tuesday as an “important step in putting a lid on Iran’s nuclear program.”

What’s bound to draw attention as the agreement’s political ramifications come into focus: Clinton owns a piece of it. She helped the negotiations get started.

The Democratic presidential front-runner said President Barack Obama – who tapped her as America’s top diplomat in his first term in office – called her late Monday night to tell her that negotiators had struck a deal: Iran will rein in its nuclear program and allow for close monitoring.

After a Tuesday morning meeting with House Democrats on Capitol Hill, Clinton tread carefully, saying she hadn’t yet been brought up to date on the specifics of the agreement.

“Based on what I know now, and I will be being briefed as soon as I finish addressing you, this is an important step in putting the lid on Iran’s nuclear program,” she told reporters after that meeting.

After her comments and between Capitol Hill meetings on Tuesday, Clinton received that briefing. Secretary of State John Kerry, Energy Secretary Ernest Moniz and National Security Adviser Susan Rice briefed Clinton and other former secretaries of state and former national security advisers.

Clinton made reference to her role in the negotiations, saying she was “part of building the coalition that brought us to the point of this agreement.”

Her top policy adviser, Jake Sullivan, sought to direct some credit toward his boss as well Tuesday morning at a breakfast hosted by the Christian Science Monitor, saying she was “centrally involved in the outset of all of this.”

RELATED: Get up to speed on the Iran nuclear talks

Clinton explained her role in the negotiations in her memoir, “Hard Choices.” She wrote that she began back-channel talks with Iran through the sultan of Oman, who had helped free American hikers imprisoned on espionage charges and suggested the nuclear talks.

She then had Sullivan, a top aide at the State Department, play a central role in getting the negotiations off the ground – flying to Oman, meeting with Iranians and eventually leading to a September 2013 phone call in which Obama and Iranian President Hassan Rouhani agreed to formally pursue the negotiations.

Her role in the Iran talks were a major reversal from the 2008 Democratic primary, in which she’d blasted Obama for agreeing to talk directly with Tehran without preconditions, saying he was “irresponsible and frankly naive.”

On Tuesday, Clinton praised her successor as secretary of state, Kerry, as well as Moniz, and said she’d ensure it is followed if she wins the 2016 presidential race.

“We have to treat this as an ongoing enforcement effort, which I certainly strongly support and as President would be absolutely devoted to ensuring that the agreement is followed,” Clinton added, leaving shortly thereafter without answering reporter questions.

Her comments come as Republicans assail the deal – and hit Obama for agreeing to it. The GOP’s presidential field roundly criticized it on Tuesday, with Florida Sen. Marco Rubio saying the President gave “concession after concession to a regime that has American blood on its hands” and former Florida Gov. Jeb Bush said it “isn’t diplomacy – it is appeasement.”

RELATED: Now that he has a deal with Iran, Obama must face Congress

It’s not yet clear whether lawmakers will even allow the White House to implement it. Republicans who control the Senate could push for a vote to block the deal. Due to some procedural wrangling in a bill earlier this year, Obama needs only 34 of the Senate’s 100 members to back him – but with Republicans all but guaranteed to oppose him and Democrats taking a cautious approach, that could be a tight vote.

Clinton said Tuesday that even with the deal in place, the United States’ problems with Tehran’s regime won’t end.

“This does put a lid on the nuclear program, but we still have a lot of concern about the bad behavior and the actions by Iran which remains the largest state sponsor of terrorism which does go after and undermine governments in the region, that poses an existential threat to Israel, that unfairly, unlawfully confines and tries Americans on trumped up charges,” she said. “That bad behavior is something we have to address.”

CNN’s Deirdre Walsh and Sophie Tatum contributed to this report.