Secretary of State Mike Pompeo said Kerry's meetings with Mohammad Javad Zarif were "unseemly and unprecedented" and "beyond inappropriate".
Obama and Kerry claimed the nuclear deal was a key achievement, though details that leaked out over weeks and months suggested the USA had repeatedly capitulated to Iran's demands.
As Trump was in the process of dismantling the Iran Deal, Kerry was overseas, pleading with leaders to try and stop the president from moving forward with the deal.
Sen. Marco Rubio (R-Fla.) wrote a letter to Attorney General Jeff Sessions on Tuesday, urging the DOJ to launch an inquiry into the actions of former Secretary of State John Kerry since the diplomat left office.
Responding to Kerry's interview on Fox News, President Trump used Twitter to suggest that Kerry had conducted "illegal meetings" with Iranian leaders, suggesting that Kerry might have violated the Foreign Agents Registration Act.
"The American people deserve to know that USA laws are enforced regardless of any individual's past position", Rubio said.
Trump withdrew the United States from Kerry's negotiated nuclear weapons deal with Iran after concluding it wouldn't prevent Iran from obtaining nuclear weapons.
The Logan Act says that any American who meets with a foreign government "without authority of the United States" to discuss anything "in relation to any disputes or controversies with the United States, or to defeat the measures of the United States", could face up to three years in prison.
The Washington Free Beacon reports that since Trump announced the USA was leaving the Iranian nuke deal, the Iranian economy "has continued to sputter and businesses and banks have exited its marketplace".
Specifically, Rubio is asking whether Kerry violated the Logan Act, which prohibits unauthorized personnel from negotiating with a foreign government in relation to any dispute with the US, according to the news network.
"You can't find precedent for this in US history, and Secretary Kerry ought not to engage in that kind of behavior", Pompeo said.