"At some point, people will decide this is not how they want to live any longer," Tillerson told CNN's Elise Labott in an interview Friday, saying "the Iranians have suffered under this regime."
"But we always support a peaceful transition of power," he cautioned. "We do not support violent transitions of power, but we do support peaceful transitions of power, and we've seen those expressions in years past with the large demonstrations at elections in 2009, the demonstrations that we see in the streets today."
Tillerson is the latest in a string of Trump administration officials to condemn the Iranian government since protests broke out across Iran last week. Vice President Mike Pence wrote in a Washington Post op-ed Wednesday
that the US "has spoken clearly and unequivocally" in support of the protesters, while US Ambassador to the UN Nikki Haley told reporters Tuesday, "all freedom-loving people must stand with their cause."
President Donald Trump has weighed in forcefully on Twitter, writing on Monday, "The great Iranian people have been repressed for many years. They are hungry for food & for freedom. Along with human rights, the wealth of Iran is being looted. TIME FOR CHANGE!"
But these calls for a change in leadership, and a decision by the administration to call for a UN Security Council meeting Friday on the demonstrations, have irked US adversaries.
Russia's mission to the UN, for example, raised the notion of the Security Council meeting about protests in Ferguson, Missouri, and Occupy Wall Street demonstrations. Russia's deputy foreign minister has called the US proposal "harmful and destructive."
The Trump administration has never been shy about criticizing the Iranian government for its interventions in foreign conflicts and continued missile development program. Trump also refused to certify Iran as compliant with the terms of a 2015 nuclear deal, putting the future of that international agreement in question.
On Friday, Tillerson reasserted the administration's intent to "look at the totality of Iran's actions and behaviors" and suggested that further non-nuclear sanctions were in the works unless "Iran alters its behavior."
He suggested that demonstrators are motivated, in part, by frustration over the same aggressive behavior that angers the US, though Iran watchers have largely attributed the protests to growing economic concerns.
"We are supportive of the Iranian people achieving their aspirations for a better quality of life, for greater freedom," Tillerson told CNN. "We believe they deserve that, but it will be up to the Iranian people to manage that peaceful transition. We support that."