March 7 (Reuters) - Uranium One Inc shareholders voted in favor of an offer from Russia's state-owned ARMZ to take it private by buying the shares it does not already own.

About 96 percent of shareholders voted in favor of the going-private transaction at a meeting on Thursday. The Russian uranium company had agreed in January to pay C$1.3 billion to take Uranium One private.

ARMZ already owns 51.4 percent of common shares in Uranium One, Canada's second-largest uranium company. ARMZ is the mining arm of Russia's nuclear regulator, Rosatom, which also builds nuclear reactors.

ARMZ still needs numerous regulatory approvals, Cantor Fitzgerald analyst Rob Chang said.

Uranium One's operations are focused in Kazakhstan, where ARMZ is also building up its asset base.

Kazakhstan is the world's top uranium producer, with more than double the output of No. 2 producer Canada in 2011, data from the World Nuclear Association showed. Its output quintupled between 2004 and 2011.

The takeover, if successful, will help ARMZ consolidate its control over uranium assets in the former Soviet Union, and strengthen access to reserves in Australia and the United States.

It will also leave just two major publicly listed, pure-play uranium producers - Canada's Cameco Corp and France's Areva SA.

Demand for uranium, used mainly as fuel for nuclear reactors, has come under pressure since the March 2011 earthquake and tsunami in Japan triggered a meltdown at the Fukushima-Daiichi atomic power plant.

The disaster led countries such as Germany and Japan to back away from nuclear power.

Some say supply and demand fundamentals are looking more favorable in the near future, with a major source of nuclear fuel supply - a longstanding program to convert highly enriched uranium from Russian warheads into reactor fuel - scheduled to end later this year. Cameco also expects a net 91 new reactors to be added worldwide by 2022.

Uranium One's privatization should lead to investors looking for exposure to uranium moving their funds into Cameco, Chang said in a note to clients. Other publicly traded uranium-focused producers include Paladin Energy Ltd, Uranium Energy Corp and Energy Fuels Inc.

Uranium One's shares were up about 1 percent at C$2.76 on Thursday afternoon on the Toronto Stock Exchange.