US President Donald Trump has signalled support for anti-government protests in Iran, but in two weeks he faces a decision on US policy toward the Islamic Republic that suddenly seems riskier than it did a week ago.

The six days of demonstrations in several Iranian cities began over economic conditions, and Trump must decide by mid-January whether to continue waiving US sanctions on Iran's oil exports under the terms of an international nuclear deal.

If he reimposes sanctions on oil, it could increase the economic pain for Iran's leaders. But analysts said it could also send the wrong message about US support for Iran's people in the middle of the boldest challenge to the leadership in a decade.

The sanctions waivers were included in the 2015 nuclear pact with Iran that eased economic pressure on Tehran in exchange for limits on its nuclear program.

Trump has repeatedly criticized the deal and promised to negotiate a better one. Reimposing oil sanctions would essentially kill the agreement.

Reviving sanctions on Iran's main export would allow Tehran to argue that the United States is ultimately the cause of Iran's economic problems, said Richard Nephew, who worked on sanctions policy at the White House under President Barack Obama.

"Let's say Trump was inclined not to renew the waivers. I think that (the protests) make it very hard for him to do that now because now that plays into the regime's hands in a way that I don't frankly think the administration is going to want to do," said Nephew, now at Columbia University's Center on Global Energy Policy.

White House spokeswoman Sarah Sanders said on Tuesday that Trump has not made a final decision on whether to waive sanctions. Asked whether the protests had changed Trump's calculation, she replied: "Not necessarily."

BLAME THE OUTSIDERS

Ray Takeyh, an Iran expert and senior fellow at the Council on Foreign Relations, said Iran's leaders will blame internal troubles on the United States and other outside powers, no matter what Washington does.

"The regime's argument that the world is against us is a constant for 38 years," Takeyh said in a telephone interview. "The optics of waiving sanctions in the midst of all this - it just doesn't look good."

Takeyh and three US officials who follow Iran said the protests undercut Iranian President Hassan Rouhani, a relative moderate who took office in 2013 pledging to improve Iran's economy, more than they threaten the country's clerical rulers.

Former CIA Director John Brennan, in a Twitter post, said the Trump administration with its condemnation of Iran and the nuclear deal over the last year has squandered an opportunity to bolster reformists in Iran and promote peaceful political change.

"Bluster is neither a strategy nor a mechanism for exercise of US power and influence," Brennan wrote.

Yet in recent days, Trump and his top aides have charted a more careful course in reacting to the demonstrations, which have led to at least 21 deaths and hundreds of arrests.

Trump in a Tweet on Tuesday called the Tehran government a "brutal and corrupt regime." But he and other US officials have shied away from suggesting Washington seeks the overthrow of Iran's Islamic theocracy, calling instead for Iranian authorities to respect protesters' rights.

State Department spokeswoman Heather Nauert on Tuesday urged Iranian security forces to exercise restraint in dealing with protests and called on Tehran to restore access to social media sites that have been restricted.

Nauert suggested the US government could impose sanctions against Iranian officials who repress peaceful protests.

Another US official said a coherent policy response to events in Iran cannot be formulated until Washington has a better understanding of the composition of the protesters, the breadth of the economic and political grievances that are driving them, and what threat they pose to the government.

The United States has had no diplomatic presence in Iran since its 1979 Islamic Revolution, limiting its ability to interpret events.

The official, speaking on condition of anonymity, said Washington's main effort now was "trying to get a sense of who is mostly behind this, how large it is and does it have legs."