This story has been updated.

Democratic presidential front runner Hillary Rodham Clinton on Tuesday called the Iranian nuclear deal announced by the Obama administration an "important step" in curtailing the country's nuclear program but stressed that the agreement will have to be "enforced vigorously, relentlessly."

"This is a very important moment. The president called me late last night to tell me that agreement has been reached. I applaud him and both Secretary Kerry and Secretary Moniz for their extraordinary efforts in bringing about this conclusion," she told reporters after a meeting with the House Democratic caucus on Capitol Hill. "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."

Clinton was on Capitol Hill Tuesday for a series of meetings with Democratic lawmakers, a gesture designed to strengthen Clinton's support among Hill Democrats, many of whom already support her candidacy. But the deal announced Tuesday has added to the importance of her marathon meetings with the various congressional Democratic caucuses.

While Clinton lauded the administration's efforts on the deal, she nonetheless voiced several concerns moving forward related to Iran's actions in the region.

"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 regions, that poses an existential threat to Israel, that unfairly, unlawfully confines and tries Americans on trumped up charges," she told reporters. "That bad behavior is something we have to address."

Rep. Steve Israel (D-N.Y.) and several other lawmakers said that Clinton had spoken in the first of her Hill meetings Tuesday about her own role in maintaining the strong sanctions against the Iranian regime that helped spur the talks. Several members who were in attendance said that Clinton sought to contextualize the deal historically, framing the agreement as the culmination of years of negotiations dating back to the Bush administration.

"She said that the core issues of the agreement are worth supporting," Rep. Steve Israel (D-N.Y.) said as he exiting the first of six huddles with congressional Democrats.

But the former secretary of state also said Tuesday that the agreement is just one step in dealing with Iran's role in the Middle East.

"Having been part of building the coalition that brought us to the point of this agreement, I think we will have to immediately, upon completion of this agreement and its rigorous enforcement, look to see how we build a coalition to try to prevent and undermine Iran’s bad behaviors in other arenas," she said.

While Clinton indicated her support for the deal’s framework, her Republican presidential rivals strongly denounced the administration’s efforts and warned that the deal would hurt U.S. interests in the region.

“President Obama’s nuclear agreement with Iran will be remembered as one of America's worst diplomatic failures,” Wisconsin Gov. Scott Walker, who officially launched his presidential campaign Monday, said in a statement. “The deal allows Tehran to dismantle U.S. and international sanctions without dismantling its illicit nuclear infrastructure—giving Iran’s nuclear weapons capability an American stamp of approval.”

Texas Sen. Ted Cruz echoed those sentiments, saying in a statement that the deal would “further arm and enrich the brutal theocratic regime that has oppressed the Iranian people for more than thirty years.” Florida Sen. Marco Rubio said administration had conceded too much: "It will then be left to the next President to return us to a position of American strength and re-impose sanctions on this despicable regime until it is truly willing to abandon its nuclear ambitions and is no longer a threat to international security.”

Former Florida governor Jeb Bush said the United States "should not base any agreements on the hope [Iranian] behavior will moderate over time... This isn’t diplomacy – it is appeasement."

Clinton plans to hold meetings with other former secretaries of state and defense before taking a final position on the deal.