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 Labour Party and even three Likud members have opposed the principle 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.
Al Jazeera's Sherine Tadros, speaking from Jerusalem, said: "Many people are pointing out the hypocrisy of these proposals.
"On the one hand, they are promoting the idea of a democratic state, while on the other hand they are completely stifling any kind of freedom of expression and freedom of speech which are implicit in those other bills, not just for Palestinians but also for Israelis.
"Many lawmakers that we have been speaking to say that if these bills are passed by the Knesset, they may be stopped by the Israeli supreme court, which will see them as unconstitutional and essentially against the law.
"And what activists are pointing out are what the proposals highlight, which is not just the nationalist and very rightwing flavour to this new Israeli government but also its determination to make the state in character a lot more Jewish and less democratic."