Washington (CNN) President Donald Trump on Monday morning continued his daily tweets on the deadly protests in Iran, calling for change to an autocratic system there that he says is rife with repression and corruption.

"Iran is failing at every level despite the terrible deal made with them by the Obama Administration," Trump wrote. "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!"

Big protests in Iran. The people are finally getting wise as to how their money and wealth is being stolen and squandered on terrorism. Looks like they will not take it any longer. The USA is watching very closely for human rights violations!

"As long as @RealDonaldTrump is POTUS and I am VP, the United States of America will not repeat the shameful mistake of our past when others stood by and ignored the heroic resistance of the Iranian people as they fought against their brutal regime ... (1/2)" Pence wrote. "(2/2) ... The bold and growing resistance of the Iranian people today gives hope and faith to all who struggle for freedom and against tyranny. We must not and we will not let them down. #IranProtests"

Iranian President Hassan Rouhani responded Monday, saying Trump has no right to sympathize with Iran because he has called the Iranian people "terrorists," according to Iran's semi-official Tasnim News Agency.

Rouhani made the comments in a meeting with lawmakers. On Sunday, state television broadcast Rouhani saying that Trump is "constantly creating problems" for Iranians, including with regard to visas and financial issues.

The leaders' tit-for-tat follows a weekend of escalating rhetoric in response to the protests and violence in Iran, with Trump warning Sunday that the United States is watching Tehran's treatment of protesters for human rights violations after anti-government protests turned deadly.

"Big protests in Iran," Trump tweeted. "The people are finally getting wise as to how their money and wealth is being stolen and squandered on terrorism. Looks like they will not take it any longer. The USA is watching very closely for human rights violations!"

Trump also took to Twitter later Sunday to criticize the Iranian government's efforts to limit access to social media.

"Iran, the Number One State of Sponsored Terror with numerous violations of Human Rights occurring on an hourly basis, has now closed down the Internet so that peaceful demonstrators cannot communicate. Not good!" Trump tweeted. The White House press office followed this with a statement saying the administration supports the right of the Iranian people to peaceful expression.

"Their voices deserve to be heard," the statement read. "We encourage all parties to protect this fundamental right to peaceful expression and to avoid any actions that contribute to censorship."

Iran, the Number One State of Sponsored Terror with numerous violations of Human Rights occurring on an hourly basis, has now closed down the Internet so that peaceful demonstrators cannot communicate. Not good! — Donald J. Trump (@realDonaldTrump) December 31, 2017

Earlier in the day, the Iranian government issued a stern warning that protesters will "pay the price" for their actions, with Interior Minister Abdolreza Rahmani Fazli saying that what he categorized as the misuse of social networks by some individuals "are causing violence and fear" and that "such behavior will be smashed," according to IRNA. Iran's official news agency.

The protests -- described as the largest public display of discontent since the 2009 Green Movement in Iran -- have emerged against a backdrop of rising food and gasoline prices.

The unrest has prompted verbal sparring between Iran and the United States, with the White House and Trump on Friday urging Tehran to respect protesters' rights.

"There are many reports of peaceful protests by Iranian citizens fed up with the regime's corruption and its squandering of the nation's wealth to fund terrorism abroad," said White House press secretary Sarah Sanders. "The Iranian government should respect their people's rights, including their right to express themselves. The world is watching."

Trump subsequently tweeted the same message.

Many reports of peaceful protests by Iranian citizens fed up with regime's corruption & its squandering of the nation's wealth to fund terrorism abroad. Iranian govt should respect their people's rights, including right to express themselves. The world is watching! #IranProtests — Donald J. Trump (@realDonaldTrump) December 30, 2017

In a pair of tweets on Saturday, Trump again addressed the protests, writing: "The entire world understands that the good people of Iran want change, and, other than the vast military power of the United States, that Iran's people are what their leaders fear the most...."

Trump continued: "Oppressive regimes cannot endure forever, and the day will come when the Iranian people will face a choice. The world is watching!"

The entire world understands that the good people of Iran want change, and, other than the vast military power of the United States, that Iran's people are what their leaders fear the most.... pic.twitter.com/W8rKN9B6RT — Donald J. Trump (@realDonaldTrump) December 30, 2017

Oppressive regimes cannot endure forever, and the day will come when the Iranian people will face a choice. The world is watching! pic.twitter.com/kvv1uAqcZ9 — Donald J. Trump (@realDonaldTrump) December 30, 2017

In the Saturday tweets, Trump posted videos of a speech he gave to the United Nations in September, in which he said , "The entire world understands that the good people of Iran want change."

Trump campaigned for president with a hard-line stance on Iran, calling the country the "No. 1 terror state" during a debate with former Secretary of State Hillary Clinton. As President, he has tried to keep that hard-line stance and announced earlier this year that he plans to decertify the Iran nuclear agreement and push Congress to a new plan to deal with Iran's nuclear program.

By weighing in on the protests, though, Trump is wading into a tricky issue that has befuddled presidents ever since the Iranian Revolution of 1979 ended relations between Washington and Tehran.

Former President Barack Obama's response to protests in Iran in 2009 was timid initially, but grew more forceful. Although those protests eventually fizzled, Obama looked to deal with Iran by minting the nuclear agreement that Trump has tried to scrap.

Obama also looked to rekindle direct talks between Iran and the United States, including in 2013, when he became the first US president to speak with an Iranian president -- Hassan Rouhani in this case -- since 1979.

Former President George W. Bush dealt with Iran more forcefully, but to mixed results, labeling the country in 2002 as part of an "axis of evil" that included Iraq and North Korea. Bush's stance was the result of a softer approach taken by former President Bill Clinton, who worked at length to foster relations with former President Mohammad Khatami.

The difficult issue that American presidents have had to confront is how to support anti-government protests in Iran without dooming those same demonstrations by allowing Tehran to paint them as closely aligned with the United States, an allegation seen in Iran as a slight.

Republican Sen. Lindsey Graham, of South Carolina, said the protests show that Obama's policies failed the region.

"The people are not getting the benefit of sanctions relief," he said on CBS's "Face the Nation." "They are more upset with their oppressors than ever. The money from sanctions relief is going to rebuilding the Iranian military and is destabilizing the Middle East."

Graham also said Trump needs to do more to help the region.

"It's not enough to watch," Graham said. "President Trump is tweeting very sympathetically to the Iranian people. But you just can't tweet here. You have to lay out a plan."

Former Republican presidential candidate Mitt Romney praised the protests in Iran, calling the protesters "heroes" in a tweet Sunday.

"Profoundly moving to watch those seeking freedom in Iran," Romney tweeted. "Patriots afar remind us of the patriots who won our own freedom and also those who preserve it. Heroes all."

Profoundly moving to watch those seeking freedom in Iran. Patriots afar remind us of the patriots who won our own freedom and also those who preserve it. Heroes all. — Mitt Romney (@MittRomney) December 31, 2017

Ambassador to the United Nations Nikki Haley said in a statement that her hopes and prayers are with "the long-repressed Iranian people," who "are now finding their voice."

"The Iranian government is being tested by its own citizens," she said in the statement. "We pray that freedom and human rights will carry the day."

Longtime diplomat and Obama National Security Council official Dennis Ross told CNN's Boris Sanchez on Monday that he thinks the Trump approach, speaking out in support of Iranian protesters, strikes the right tone.

Ross said the Obama administration initially received messages from those in the Green Movement in Iran to "keep it cool" in order to prevent Tehran from claiming the unrest was foreign-inspired.

"And I think in retrospect, we made a mistake," he said. "I think we should have made it clear that, in fact, the world was watching."