The US will soon impose further costs on the perpetrators of violence against peaceful demonstrators who protested against the death of a 22-year-old woman in the custody of the morality police in Iran, President Joe Biden has said, as he expressed grave concern over the crackdown on them.

Mahsa Amini, a 22-year-old from Iranian Kurdistan, was arrested for allegedly violating the country's strict Islamic dress code.

The custody death of Amini on September 13 in Tehran sparked street protests around the country. Iranian Security forces have cracked down on the protests.

"For decades, Iran's regime has denied fundamental freedom to its people and suppressed the aspirations of successive generations through intimidation, coercion and violence. The United States stands with Iranian women and all citizens of Iran who are inspiring the world with their bravery," President Biden said on Monday.

Biden said the United States is making it easier for Iranians to access the internet.

"The US is also holding accountable Iranian officials and entities, such as the morality police, that are responsible for employing violence to suppress civil society," he said on Monday.

"This week, the United States will be imposing further costs on perpetrators of violence against peaceful protesters. We will continue holding Iranian officials accountable and supporting the rights of Iranians to protest freely," Biden said in a statement.

Iran's state TV has reported that the death toll from violent clashes between protesters and Iranian security officers could be as high as 41. Rights groups have given higher death counts. Several people have been apprehended, with local officials reporting at least 1,500 arrests.

"I remain gravely concerned about reports of the intensifying violent crackdown on peaceful protests in Iran, including students and women, who are demanding their equal rights and basic human dignity," Biden said.

They are calling for just and universal principles, which underpin the UN Charter and Universal Declaration of Human Rights, he added.

White House Press Secretary Karen Jean-Pierre told reporters on board Air Force One that the US is alarmed and appalled by reports of security authorities responding to university students' peaceful protests with violence and mass arrests.

"University students are the talented young people who should be the future of Iran. They are rightly enraged by the death of Mahsa Amini, the Iranian government's treatment of women and girls and the ongoing violent crackdown on peaceful protests," she said.

"This weekend's crackdowns are precisely the sort of behaviour that drives Iran's talented young people to leave a country by the thousands to seek dignity and opportunity elsewhere," Jean-Pierre said.

Responding to a question, the press secretary said the Joint Comprehensive Plan of Action (JCPOA) is the best way to address the nuclear problem with Iran.

"As long as we believe pursuing JCPOA talks is in the US national security interest, we will do so," she said, adding that the US will continue to use other tools to address other problems with Iran's behaviour.

The JCPOA, commonly known as the Iran nuclear deal, is an agreement on the Iranian nuclear programme reached in 2015 between Iran and the five permanent members of the United Nations Security Council China, France, Russia, United Kingdom, United States plus Germany and the European Union.

Under its terms, Iran agreed to dismantle much of its nuclear program and open its facilities to more extensive international inspections in exchange for billions of dollars worth of sanctions relief.

Former president Donald Trump unilaterally withdrew from the agreement in 2018. The US and Iran's indirect talks to revive the pact have broken down.

Iran has long denied it is seeking to develop nuclear weapons while saying it has a right to civilian nuclear infrastructure.

"You've heard this from the National Security Advisor, Jake Sullivan, that even though we are engaged in nuclear negotiations, we're not going to slow down one inch in our defence and advocacy for the rights of the women and the citizens of Iran," Jean-Pierre said.

"Even at the height of the Cold War, as President Reagan was calling the Soviet Union an evil empire, he was engaged in arms control talks," Jean-Pierre said.