Trump has tweeted several times over the last few days in support of the anti-government protests, comments that have angered many Iranians given his travel ban barring them from getting USA visas, as well as his comments over the nuclear deal.
Iran is failing at every level despite the bad deal made with them by the Obama Administration.
"The Iranian authorities must respect the rights of all demonstrators and detainees, including their right to life, and guarantee their safety and security", Zeid Ra'ad al-Hussein said in a statement.
"We have no information yet whether it was protesters or the police that fired yesterday [Sunday] and the issue is under investigation", the report quoted him as saying. Protesters have chanted against Rouhani as well as Supreme Leader Ayatollah Ali Khamenei.
The protests apparently were triggered by a surge in prices of basic food supplies, which also had contributed to early Arab Spring protests six years ago.
Iranian officials have downplayed the strength of the protests.
At least 10 people have been killed in nationwide protests in Iran over the past five days, Iranian state television said yesterday, a day after President Hassan Rouhani appealed for calm and urged demonstrators to refrain from violence.
Iranian state media yesterday aired pro-government demonstrations in cities across the country after a week of protests and unrest over the nation's poor economy - a move apparently seeking to calm nerves amid clashes that have killed 21 people.
Officials said two people were killed when what were described as rioters seized a fire engine and then crashed into two other vehicles.
Some of the early protests in Mashhad reportedly were organized by ultra-hard-line regime supporters opposed to Rouhani, and may have been created to undermine his authority.
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Despite a billion dollars released to Iran by the United States, inflation is worsening and unemployment remains high among young people.
Hundreds of students and others joined a new economic protest at Tehran University, with riot police massing at the gates as they shut down surrounding roads. Finally, the regime is downplaying the power and significance of the protests.
"Some armed protesters tried to take over some police stations and military bases but faced serious resistance from security forces", state TV reported.
US President Donald Trump continued to tweet on the protests despite criticism from many Iran experts that his comments are counterproductive. This will more likely cause more people to become disaffected with the regime. The world is watching! Trump's words also make it easy for the Iranian regime to dismiss their protests as American-inspired.
The rising death toll comes as spontaneous demonstrations have swept across Iran since last Thursday, when economic protests swiftly turned political and took aim at the government. "The clerics act like God".
Economic hardship has worsened despite the lifting of sanctions against the Iranian government in 2015 by the Obama administration.
"We all know that's complete nonsense", said Nikki Haley, the USA ambassador to the United Nations.
Where will the protests lead? I was visiting Iran during the Green Movement, where people were protesting against the rigged election and chanting "where is my vote".
James Phillips is the senior research fellow for Middle Eastern affairs at the Douglas and Sarah Allison Center for Foreign Policy Studies at The Heritage Foundation.