The bill curbing Supreme Court review of some government decisions passed in a stormy Knesset parliament on Monday after a walkout by lawmakers.
Protest leaders said growing numbers of military reservists would no longer report for duty if the government continued with its plans.
First elected to top office in 1996 and now in his sixth term, Netanyahu, 73, is facing his biggest domestic crisis.
A Lebanese source familiar with the development said the men were members of a Hezbollah elite unit on a patrol that had nothing to do with Israel's domestic crisis.
Hezbollah leader Hassan Nasrallah on Monday said Israel's domestic crisis showed it was on a "path of collapse and fragmentation".
Persons:
Netanyahu, Benjamin Netanyahu, Yair Lapid, Zion Hagay, Kan, Corinna Kern, striding, Hassan Nasrallah, Bezalel Smotrich, Dan Williams, Ari Rabinovitch, Henriette Chacar, Andrew MacAskill, Laila Bassam, Tom Perry, Andrew Cawthorne, Nick Macfie
Organizations:
Israeli Democracy, Israel Bar Association, Israel Medical Association, Health Ministry, REUTERS, BANK, Orthodox Jewish, West Bank, Hamas, Hezbollah, Finance, Army Radio, Thomson
Locations:
JERUSALEM, Israel, Histadrut, United States, Britain, Jerusalem, Tel Aviv, Washington, Nablus, Palestinian, Lebanese, Iran, London, Beirut