Four days of demonstrations in Iran represented the most daring challenge for clerical leadership after the 2009 pro-reform unrest. At least four people were killed while some clashes with the police were really violent.
"I can only wish the Iranian people success in their struggle for freedom and democracy," Israeli intelligence minister Ysrael Katz said in an interview on army radio.
"If people can achieve freedom and democracy, many of the threats to Israel and the entire region will disappear."
Israel has long expressed alarm over the nuclear program of the Shiite power and its support for the Islamist guerrillas in Lebanon and the Palestinian territories - concerns shared by the Sunni Arab states.
Asked why Israeli Prime Minister Benjamin Netanyahu did not follow US President Donald Trump's lead in offering more open support to protesters, Katz said, "Israel has pledged not to get involved in this internal affair."
Trump's harsh approach to Tehran, which included the threat of US sanctions, disrupted the Iranian government's "illusion of economic improvement," he said.
On Sunday, an Iranian official accused "foreign agents" of a clash in which two demonstrators were killed.
Katz denied these accusations and sent the accusations back to the sender as "a mendacious and propaganda regime".