Amini, 22, was pronounced dead on September 16, days after the notorious morality police detained the Kurdish Iranian for allegedly breaching rules forcing women to wear hijab headscarves and modest clothes.
Anger over her death has sparked the biggest wave of protests to rock Iran in almost three years, with security forces in Tehran cracking down Sunday night on hundreds of university students.
"This week, the United States will be imposing further costs on perpetrators of violence against peaceful protestors," Biden said in a statement.
"We will continue holding Iranian officials accountable and supporting the rights of Iranians to protest freely."
Biden added he was "gravely concerned" about reports of the intensifying repression of protesters and said Washington stood with "all the citizens of Iran who are inspiring the world with their bravery".
Biden gave no indication of what measures he was considering. Iran is already under crippling US economic sanctions largely related to its controversial nuclear programme.
White House Press Secretary Karine Jean-Pierre earlier on Monday stressed that the "problems with Iran's behaviour" are separate from efforts to revive the 2015 nuclear accord, which Washington will pursue "as long as we believe" it is in US national security interests.
Iran's supreme leader Ayatollah Ali Khamenei had accused arch-foes the United States and Israel of fomenting the upheaval.
The riots "were engineered by America and the occupying, false Zionist regime, as well as their paid agents, with the help of some traitorous Iranians abroad", the Islamic republic's leader said.
In his first public comments on Amini's death, 83-year-old Khamenei stressed that police must "stand up to criminals".
Khamenei said "some people, without proof or an investigation, have made the streets dangerous, burned the Koran, removed hijabs from veiled women and set fire to mosques and cars".
He added that "this is not about hijab in Iran", and that "many Iranian women who don't observe the hijab perfectly are among the steadfast supporters of the Islamic republic."
Concern grew over a night-time crackdown on students at Tehran's prestigious Sharif University of Technology where, local media reported, riot police carrying steel pellet guns used tear gas and paintball guns against hundreds of students.
"Woman, life, liberty" the students shouted, as well as "students prefer death to humiliation", Mehr news agency reported.
Oslo-based group Iran Human Rights posted videos apparently showing police on motorcycles chasing students running through an underground car park and taking away detainees, their heads covered in black cloth bags.
In one clip, which IHR said was taken at a Tehran metro station, a crowd can be heard chanting: "Don't be afraid! Don't be afraid! We are all together!"
In response to the university protests, German Foreign Minister Annalena Baerbock said the courage of the Iranians was "incredible", and that the "regime's brute force is an expression of sheer fear of the power of education and freedom."
British Foreign Minister James Cleverly said the violence against protesters was "truly shocking", and summoned Tehran's top diplomat in London, while Canada imposed new sanctions citing "the egregious actions committed by Iran's so-called 'Morality Police'".
Protests were also reported at other universities, including in the central city of Isfahan.
Iran has repeatedly accused outside forces of stoking the protests and last week said nine foreign nationals -- including from France, Germany, Italy, the Netherlands and Poland -- had been arrested.
The parents of Italian woman Alessia Piperno, 30, from Rome, said they had lost contact with her after speaking to her on Wednesday -- her birthday -- but then received a phone call from her on Sunday apparently from detention.
"I'm fine but there are people here who say they have been inside for months and for no reason," she told them, according to Il Messaggero, Rome's daily newspaper. "I fear I won't be let out again. Help me."
Italy's foreign ministry has so far made no comment on the identity of the Italian held.
At least 92 protesters have been killed so far in the Mahsa Amini rallies, said IHR, which has been working to assess the death toll despite internet outages and blocks on WhatsApp, Instagram and other online services.
Amnesty International said earlier it had confirmed 53 deaths, after Iran's semi-official Fars news agency said last week that "around 60" people had died.
At least 12 members of the security forces have been reported killed since September 16.