Netanyahu, who also chastised European governments for not being supportive enough of the protests, also said: "when this regime finally falls, and one day it will, Iranians and Israelis will be great friends once again".
In an apparent attempt to stave off more unrest, the authorities began blocking access to photo sharing and online messaging services on mobile phones, including Telegram, which the government accused of being used to foment violence, local media and Telegram's CEO said.
They began as demonstrations against economic conditions in second city Mashhad on Thursday, but quickly turned against the Islamic regime as a whole with thousands marching in towns across Iran amid chants of "Death to the dictator".
A protester shot and killed an Iranian policeman on Monday, marking the first death among the security forces amid ongoing anti-government demonstrations, according to the police and media reports.
State TV said armed demonstrators had tried and failed to seize police and military bases.
Iranian Judiciary Chief Ayatollah Sadeq Amoli Larijani on Monday ordered the country's prosecutors to take serious measures in dealing with the rioters vandalizing public properties amid the recent civil protests. The Fars news agency reported "scattered groups" of protesters in Tehran on Monday and said a ringleader had been arrested.
Meanwhile on Sunday, an Iranian anti-regime protester said over Israel's Channel 10 that the Iranian people are "taking to the streets spontaneously in most cities in Iran" and have concluded that they must "get to the root" of Iran's problems, "the regime and the leadership".
Hundreds of people have been arrested and a prominent judge warned on Tuesday that some could face death penalty trials.
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Unsigned statements on social media urged Iranians to continue to demonstrate in 50 towns and cities.
Earlier on Monday, Iranian state TV said 12 people had been killed amid the nationwide protests.
He blamed the US, Israel, and Saudi Arabia for involvement in the unrest in order to destabilize the country.
"I do not know whether yesterday's shooting was done by rally participants or the police and this issue is being investigated", Khademi was quoted by ILNA as saying. "They are hungry for food & for freedom".
Regional governor Mostafa Samali told Fars that only one person was killed in an incident unrelated to the protests, and the suspected shooter had been arrested.
"I wish the Iranian people success in their noble quest for freedom", he said in a video posted on his Facebook page.
According to Article 27 of the Iranian Constitution, "public gatherings and marches are allowed so long as the participants do not carry arms and are not in violation of the fundamental principles of Islam".
He added that "after the confrontation of the past days it is all the more important for all sides to refrain from violent action".