The legislation proposes creating a formal list of extremist groups and their members. It would also give courts in the capital Astana the authority to designate groups as extremist.
If Nazarbaev signs the bill, law enforcement agencies and the Prosecutor-General's Office will be granted expanded surveillance rights as the power to disband organizations suspected of extremism.
Rights groups are alarmed by the bill, which they say lacks a precise definition of extremism and could be used to prosecute opposition groups, NGOs, and minority religious organizations that may not be mainstream -- but are not extremist.
Speaking to RFE/RL in Astana today, Kazakh lawmaker Serik Abdrakhamov gave his definition of an extremist group.
"Any group calling for liquidation of a legitimate power structure should be defined as an extremist organization," Abdrakhamov said. "Also, all those who are causing interethnic hostility."
Ninel Fokina heads the Almaty Helsinki Committee, a member of the International Helsinki Federation for Human Rights. She told RFE/RL she has little doubt Nazarbaev will sign the bill, which she said will put Kazakhstan's civil society and independent media at risk of being placed under government control.
"[The bill] introduces censorship in practice, because it says designated government bodies are given the right to monitor all print and Internet publications and prevent the publication of any material that has what the bill calls an "anti-constitutional nature," Fokina said. "Actually, the bill is medieval. It's raised a lot of objections."
Fokina said the recent closure of the country's main opposition party is an example of the government using claims of unconstitutional activity as a pretext for suppressing its rivals.
The Democratic Choice of Kazakhstan (DCK) has regularly leveled corruption allegations against top politicians, including Nazarbaev. The party lost a long legal battle on 9 February, when a city court in Almaty ordered its dissolution.
Officially, the DCK was banned for breaching Kazakhstan's national security laws by calling for street protests following last September's parliamentary elections, which many opposition supporters say were rigged in favor of pro-government candidates.
Kazakh opposition leaders and rights activists say the case against DCK is politically motivated and represents a threat to all opposition parties.
Andrei Kravchenko of the Kazakh Prosecutor-General's Office said the religious group Hizb ut-Tahrir and others like it are also likely to appear on any future list of extremist organizations.
"If this draft bill is adopted, then all the Hizb ut-Tahrir-type organizations will also be banned from the territory of Kazakhstan," Kravchenko said.
Hizb ut-Tahrir -- or the Party of Liberation -- is an international Islamic organization that seeks to establish a caliphate, or Islamic state, in the Ferghana Valley, a region that extends across Uzbekistan, Kyrgyzstan, and Tajikistan. It claims to disavow violence.
Uzbekistan, Kyrgyzstan, and Tajikistan -- which have all witnessed attacks by Islamic militants -- have all banned the group as an extremist organization, as has Russia. Thousands of Hizb ut-Tahrir members have been detained in those countries in recent years.
Kazakhstan, by contrast, has witnessed no attacks by Islamic militants and currently has no official ban on Hizb ut-Tahrir. But Nazarbaev recently urged tougher security measures, saying the group -- which Uzbekistan blames for deadly attacks there last year -- is now stepping up its activities in Kazakhstan.
Fokina said Kazakh authorities recently launched a campaign against Hizb ut-Tahrir. Vadim Berestov, a senior member of the group from the southern city of Shymkent, last month was sentenced to a year in jail.
It's a relatively light sentence compared to Uzbekistan, where Hizb ut-Tahrir members often receive prison sentences of 15-20 years. But Kazakh courts are expected to begin handing down much stiffer sentences if the parliament's bill is signed into law and Hizb ut-Tahrir is qualified as extremist.
Fokina of the Almaty Helsinki Committee said the extremism bill will give Kazakh authorities the power to ban not only Hizb ut-Tahrir or local opposition groups, but even prominent international human rights organizations.
"According to one clause [of the bill], an organization can be qualified as extremist if any of its branches have already been qualified as extremist," Fokina said. "Authorities can use information they get from the special services of other countries. For example, I'm a member of the International Helsinki Federation, which has its headquarters in Vienna and 38 branches in different countries -- including one in Uzbekistan headed by Talib Yakubov. If the Uzbek security service informs the Kazakh prosecutor's office that Yakubov is qualified as an extremist [in Uzbekistan], which they can easily do, then a Kazakh court can qualify all of the International Helsinki Federation -- including me -- as extremist."
Fokina said the Belarusian and Turkmen branches of the Helsinki Federation also risk being qualified as extremist -- and ultimately put the entire organization under threat. Both branches have been highly critical of their countries' regimes.