'Lieberman's continuous intolerable statements undermine the government's image and achievements, primarily harming Prime Minister Netanyahu,' Herzog said.
'It should be made clear to Lieberman, who is motivated by a narrow political agenda, that his ongoing remarks are not in the state's best interest,' Herzog added.
Labour Party legislator Yuli Tamir said Lieberman should resign.
'It is unthinkable that the Israeli government will have a senior minister with a racist agenda, which is discriminatory against large parts of the population,' she said.
Arab-Israeli legislator Taleb el-Sana said simply that Lieberman was 'out of his mind' and noted that the proposal, if implemented, would be rejected by the Supreme Court.
A foreign ministry employee, who did not wish to be named, told the Y-Net news site that she thought Lieberman's proposal would never be implemented.
'Luckily, there are laws in the country, including laws against discrimination, and a person can't change the way of the world with the stroke of one statement,' she said.
'In general, the foreign minister makes all kinds of statements, and I have stopped being outraged by them. That's who he is, and he looks for provocations. It is not a statement with any thought behind it,' she said.