MOSCOW/NEW DELHI, Nov 16 (Reuters) - Russia handed over a $2.3 billion aircraft carrier to India on Saturday after years of delays, extending the South Asian country's maritime reach in the Indian Ocean as it looks to counter China's assertive presence in the region.

The handover, at a shipyard near the Arctic Circle, underlined close defence ties between Russia, the world's No. 2 arms exporter, and the world's largest arms customer, India.

But while India remains Russia's biggest buyer, it has started to look to new military suppliers and aims to build more hardware itself. It has recently rolled out new military purchase rules to lure local private companies into the sector.

The retooled Soviet-era ship was commissioned into the Indian Navy at the Sevmash shipyard in Severodvinsk, on the White Sea, in a ceremony attended by Russian Deputy Prime Minister Dmitry Rogozin, and Indian Defence Minister A.K. Antony.

The ship, built in the final years of the Soviet Union and named the Admiral Gorshkov, will now be escorted by warships to to India in a two-month voyage from Russia's northern coast. It has been renamed INS Vikramaditya.

A recent upgrade means that the carrier, originally designed to carry Yak-38 vertical take-off aircraft, has been requipped to carry Mig-29K fighter jets. It can carry up to 30 aircraft and will have a crew of around 2,000.

India signed a deal to buy the carrier in 2004 after a decade of negotiations. Its reconditioning was to be finished in 2009, but the price was increased and delivery postponed until 2012 under a new agreement, according to the Indian navy.

The handover was later delayed by another year.

India's first, British-built, aircraft carrier was bought in the 1960s and was decommissioned in 1997. Another ex-British carrier, the INS Viraat, is in operation but is reaching the end of its service.

India is on a push to modernise its mostly Soviet-era military, and plans to spend $100 billion in the next 10 years doing that. It buys about 60 percent of its arms needs from Russia, but has started a diversification drive recently.

China last year put its first-ever aircraft carrier, another retooled Soviet-made craft called the Liaoning, into service amid tensions with Japan over contested islands and a show of strength in the South China sea.

India launched its first domestically-built aircraft carrier this year, but it will not be fully operational until 2017. (Reporting by Anurag Kotoky, additional reporting by Jason Bush; Editing by Mike Collett-White and Ralph Boulton)