"The security agencies have been ordered to deal with this case, investigate it and act with the utmost speed to bring to justice what appears to be another underground," Olmert told his cabinet in broadcast remarks.
Professor Zeev Sternhell, a political scientist at Jerusalem's Hebrew University and a leading opponent of settlement building in the Palestinian territories, was slightly wounded on Thursday when a pipe bomb exploded outside his home.
Police found posters in his Jerusalem neighborhood offering a one million shekel ($294,000) reward to anyone killing a member of Israel's Peace Now movement that opposes Jewish settlement on land occupied in the 1967 Middle East war.
Olmert compared the bombing with the 1995 assassination of Prime Minister Yitzhak Rabin by a Jewish ultranationalist and a hand grenade attack that killed a Peace Now activist in 1983.
"A bad wind of extremism, hate, evil, violence and contempt for state authorities is blowing through certain sectors of the Israeli public and threatening Israeli democracy," said Olmert, who is engaged in land-for-peace talks with the Palestinians.
In the 1980s, a Jewish underground group, acting after six Jewish seminary students were killed in a Palestinian attack, carried out bombings that maimed several West Bank mayors and a shooting in an Islamic college that killed three students.
Members of the group were jailed but the sentences were later commuted by then-President Chaim Herzog.
Olmert, who resigned a week ago in a corruption scandal, is serving in a caretaker capacity until a new Israeli government is formed. His deputy, Foreign Minister Tzipi Livni, is trying to put together a governing coalition.
