The protests, which vented anger at high unemployment and official corruption, were the largest seen in Iran since the disputed 2009 presidential election, and some demonstrators called for the overthrow of the government.
Different security and intelligence forces detained the protesters, making it hard to know the exact number of detainees, Sadeghi was quoted as saying.
The number is far higher than the 450 people Iranian authorities previously said were detained. "We fully support the fearless Iranian people who are protesting these heinous actions".
Protests over food prices and other economic problems began December 28 in Iran's second-largest city of Mashhad, where the provincial government of the northern region of the city said 85 percent of detainees there were released after signing a pledge not to re-offend.
Officials have said the majority have since been released, with only the main "instigators" facing trial.
On Monday, state-run Aftab News reported that Sina Ghanbari died in custody after being held in Tehran's notorious Evin Prison along with hundreds of other protesters.
The Trump administration, Sanders said, was "deeply concerned" by reports that the Iranian regime has imprisoned thousands of its citizens in the last week for protesting against the government.
Authorities also have deployed additional police and members of the Basij, a volunteer organisation affiliated with Iran's paramilitary Revolutionary Guard.
UK Foreign Minister Boris Johnson told the British Parliament Tuesday that "it is vital that the people of Iran and government of Iran should understand that we in this country support right to peaceful demo within the law".
An Iranian lawmaker publicly announced Thursday that the hardline Islamic regime has detained over 3,700 protesters and demonstrators -many of them students- in an attempt to quash the nationwide riots that stunned leaders in Tehran, reports Fox News.
USA officials and analysts studying Iran say believe conservative opponents of President Hassan Rouhani, a relative moderate within Iran's clerically overseen government, started the demonstrations in Mashhad, but quickly lost control of them.
"We should differentiate between people's righteous and honest demands on one side and barbaric and disruptive moves by another group", he said.