Graham warned that the US has a chance to "deliver some fatal blows to really bad actors" in the new year, but that the international situation is precarious.
"If we blink, God help us all," he said.
The protests began last Friday NZT in response to economic woes in Iran, where growth unrelated to renewed oil exports has lagged significantly since international sanctions were lifted as part of the 2015 nuclear deal.
As the protests spread, demonstrators have used them to highlight a variety of other problems, including government corruption and the need for reforms.
The escalating unrest poses a challenge for Iranian President Hassan Rouhani, a moderate who appealed to reformists when he was re-elected in May by a landslide. Some have interpreted the protests as a response to Rouhani's failure to deliver on key economic promises he made after the nuclear deal.
The last major wave of protests followed Iran's disputed presidential election in 2009.
Graham spoke after two Iranian demonstrators were confirmed killed in the protests. Local media reported that about 200 people were arrested in Tehran yesterday and showed images of police firing a water cannon at demonstrators in the city centre.
Today, Iranian authorities blocked Instagram and the popular messaging app Telegram. Their intention was to "maintain peace," according to state television, but protesters saw the move as a direct crackdown on their efforts, which have been fuelled by publicity on social media.
Trump has tweeted several times in support of the demonstrators, writing that the United States is "watching very closely for human rights violations".
"Big protests in Iran. The people are finally getting wise as to how their money and wealth is being stolen and squandered on terrorism," Trump wrote. "Looks like they will not take it any longer."
Graham, who said it's "not enough to watch" and post on Twitter, called the protests evidence of former President Barack Obama's foreign policy failures.
"It tells us that the Obama approach of relieving sanctions . . . has failed," he said.
THE PROTESTS: WHAT SPARKED THEM?
