Sponsored by Zevulun Orlev, an Israel Beiteinu MK, the bill stipulates one-year imprisonment of any person who makes "such public statement".
The bill is part of two draft laws proposed by the Israel Beiteinu.
The first is the Loyalty Oath Law that obliges all Palestinian Israelis to pledge allegiance to the Jewish identity of the state.
The second is the Nakba Law, which bans commemoration of the 1948 dispossession of the Palestinians as a result of the creation of Israel.
Israel Beitenu, led by Avigdor Lieberman, the Israeli foreign minister, grew to be Israel's third largest political party in the February election, reflecting a shift to the right by the Israeli public.
Rights in jeopardy
Aljazeera's senior political analyst Lamis Andoni said the two bills will jeopardise the rights of Palestinian Israelis.
"The two bills, if finally ratified, would punish Palestinian Israelis, and delegitimise their existence inside Israel," she said.
"It is considered a prelude to the expulsion of the Palestinian Arabs as advocated by many Israeli leaders."
The Meretz Party, several Knesset members of the Labor Party and even three Likud members have opposed the principal of both bills.
The bill has to pass three votes and a committee review before taking effect as a legislation.
A similar bill was presented by Lieberman's deputies in 2007 but blocked by the parliament.