A few months after the law came into force in July 2002, he waived some of the restrictions for former Soviet citizens who were officially registered in Russia at the time.
As a result, citizens of former Soviet countries became entitled to receive Russian citizenship without, for example, having lived in Russia for five years without interruption or having passed a Russian-language test.
The simplified procedure, however, was temporary and applied only to those who filed their naturalization requests by 1 January 2006.
The latest presidential amendments introduced this week to the State Duma propose to extend this deadline by two years. But most significantly, they would allow all former Soviet citizens legally living in Russia -- and not just those registered before the citizenship law came into force in July 2002 -- to apply for fast-track citizenship.
Akhmed Bilalov, deputy head of the State Duma's committee for affairs related to the Commonwealth of Independent States, said he will back the amendments.
He said the simplified rules will help reunite families whose members were granted different citizenships following the collapse of the Soviet Union.
The bill, he added, would also help Russia attract much-needed migrant workers from its former Soviet neighbors.
"Today a kind of fight for migration flows is going on, and Russia is also interested," Bilalov said. "Of course, it will be more interesting for us if [migrants] are our former countrymen, who have a similar education to that of Russians. Citizens of the former Soviet Union have the same education, cultural upbringing, and public world outlook."
Russia has a particularly tough immigration policy that prevents -- or at any rate discourages -- millions of migrant workers from seeking to gain legal status.
In the face of a looming demographic crisis, however, Russia seems increasingly eager to open its doors to migrants to compensate for its alarming population decline.
According to Russian Finance Minister Aleksei Kudrin, Russia's population will fall by 1 million people annually over the next 20 years.
The fact that the Federal Migration Service last month announced plans to legalize about 1 million illegal immigrants next year comes as a further sign that the government is taking steps to ease immigration rules.
Putin's bill, however, has left migration experts cold.
Svetlana Gannushkina, a leading migrant-rights activist who heads the Civil Assistance Committee rights group, says the proposed changes will not bring much improvement for immigrants.
The proposals, she laments, do not address Russia's complicated residency-registration procedure, which in the new draft law remains a key condition for obtaining Russian citizenship.
"We are somewhat disappointed that the president has limited himself to this, because we hoped that more significant amendments would be introduced to this law, where the right to obtain citizenship is based on the possession of a residency registration," Gannushkina said. "Permanent residency is something material that can lead to [the obtaining of] rights. Registration can only confirm rights, but it cannot be a source of rights. Unfortunately, our authorities do not seem to understand this."
Yelena Tyuryukanova, a migration expert at the Russian Academy of Sciences' Institute for Socioeconomic Problems, welcomed the amendments. She sees them as another small step toward improving the status of migrant workers and their families, although she accuses Russia of dragging its feet on easing immigration.
She told RFE/RL that the government's reluctance to make more significant concessions to immigrants shows that Russia still lacks a clear immigration policy.
"[Russia's] position is strange, it is not thought through," Tyuryukanova said. "On the one hand they [authorities] are afraid of opening the door, of easing the process of obtaining citizenship, but obviously very strict measures cannot be taken either, since the policy -- in principle -- is directed toward accepting migrants. There is no governmental conception yet. This is why fragmentary measures are taken, and so far the whole [immigration] policy consists of these fragments, like a scattered mosaic."
Putin's proposal has also angered nationalists, who say that former Soviet citizens should not benefit from privileges over other foreigners.
Dmitrii Rogozin, the leader of the nationalist-patriotic party Motherland (Rodina), told reporters yesterday that only ethnic Russians who hold a foreign passport should be entitled to a simplified naturalization procedure.
The State Duma is expected to vote on the amendments by the end of this year.