They said the new law is designed to limit the numbers of Arabs living in the Jewish state, rather than being motivated by security concerns
Ibrahim Hauari, deputy mayor of the northern Israeli town of Maalot-Tarshiha, said on Tuesday the government should have the guts to own up to their hidden agenda.
Hauari said he married his wife, from the West Bank town of Jenin, in 1998 and she was on the verge of being granted citizenship.
"After we got married in 1998, we applied for Israeli citizenship, which usually takes five years to obtain. With this new law, she won't get it," he said.
"It's ironic it should happen here and to me. I work for a mixed Arab-Israeli town where we've always promoted co-habitation."
He added he is worried the police will come and take his wife back to Jenin once her temporary permit issued a year ago ends in six months.
"This is paramount racism. This law contradicts human rights and has no equivalent anywhere else in the world," said Hauari.
The Israeli Arab rights group Mossawa have said 21,000 families will be affected by the Citizenship Law that was passed last Thursday.
The law was approved for one year and only applies to Palestinians and not foreigners married to Israelis.
"This is paramount racism. This law contradicts human rights and has no equivalent anywhere else in the world"
Meanwhile, Samia Diab from Arab east Jerusalem said she feared she would find it impossible to leave Israel under the legislation even though she has an Israeli identity card.
"I can't travel outside Israel because one condition for my applying for Israeli citizenship was to surrender my Jordanian passport," she said.
"It's so obvious that this law is pure discrimination and dictated by Israel's wish not to have more Arabs living inside Israel so that it can stay mainly Jewish."
Her Israeli Arab husband Samer said that the new law meant Samia was trapped in Israel.
He said: "She is from east Jerusalem and has a permanent Israeli ID but can no longer hope to become an Israeli citizen with that law."
Israeli Interior Minister Avraham Poraz admitted on Monday he is unhappy with the law but said security concerns outweighed human rights.
"I'm not happy with the law... because most (Palestinians) have no intention to be involved in terrorism," he said.
"But even though their human rights are affected, our obligation to prevent terrorism is on a higher scale."
The push for the legislation stemmed from an attack carried out in the northern city of Haifa by a Palestinian who acquired citizenship by marrying an Israeli Arab woman.
The minister in charge of relations with parliament, Gideon Ezra, argued that 30 Israelis were killed by Palestinians who had gained Israeli citizenship through marriage since the start of the intifada 34 months ago.
Israel's Arab community accounts for 18 percent of the country's population.