The submarine, one of the Russian navy's most advanced vessels, sank in the Barents Sea on 12 August, 2000 with the loss of all 118 people on board.
An explosion of fuel from an old torpedo caused the disaster.
Moscow's response to one of the greatest disasters in Russian naval history was widely criticised.
Relatives and members of Russia's northern fleet are due to cast wreaths into the sea on Thursday in memory of the crew.
Flags are being flown at half-mast at the headquarters of all Russia's naval fleets, and a ceremony and minute's silence was being held at Moscow's Central Army Museum.
The initial response to the disaster in 2000 was shambolic, says the BBC's Richard Galpin.
After radio contact was lost there was a still unexplained delay before a search and rescue mission was launched.
Although the submarine was lying just 100m below the surface of the sea, attempts to locate it and reach it repeatedly failed.
It was days before the authorities informed relatives that something was wrong and the then President, Vladimir Putin, initially remained on holiday.
Russia eventually accepted international assistance, but when Norwegian divers opened the Kursk's hatch 10 days later they found the boat flooded and everyone dead.
Many had died within seconds of the initial explosion, but others survived for several hours, a report found.
Russian officials originally suggested the submarine may have collided with a foreign ship or with a stray mine.
But it emerged that an explosion was caused by fuel that had leaked from a torpedo.
This started a fire, which subsequently caused all ammunition on board to detonate.
The boat was raised and the bodies recovered in 2001.

Maureen Greaves, a Church Army lay preacher, received the honour in recognition of her services to the community in north Sheffield.
She said: "I couldn't believe the work I do would warrant such an honour."
Alan Greaves was attacked in 2012 as he walked to his church in Sheffield, dying a few days later.
Despite her loss Mrs Greaves said she had been determined to keep her up the charity work among the community.
"Being involved in a murder and a trial, it was good to come back to work, it took my mind off it."
Mrs Greaves said: I have a strong Christian faith and that enabled me to do it."
She and her husband set up a food bank for families with limited income in the garage of the couple's home.
They then took over a shop to improve distribution to those most in need just weeks before his death.
Mr Greaves suffered "catastrophic" injuries when he was battered with a pick-axe handle.
The retired social worker was walking to St Saviour's Church to play the organ for the service, something he had done for 40 years, when he was attacked.
The father-of-four died three days later in hospital from serious head injuries.
Jonathan Bowling, 22, was jailed for life after pleading guilty to the murder.
Ashley Foster, 22, of Wesley Road, High Green was sentenced to nine years for manslaughter after a jury cleared him of murder.

The stamps will feature characters such as Darth Vader, Luke Skywalker and Yoda and will also feature three scenes from the new film, Star Wars: Episode VII - The Force Awakens.
They will go on sale on 20 October.
Ceremonies are being held in Russia and on board its naval vessels to commemorate the 10th anniversary of the Kursk nuclear submarine disaster.
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The widow of a church organist beaten to death on Christmas Eve has been appointed MBE in the Queen's Birthday Honours list.
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Eighteen new first class stamps are being released by the Royal Mail to celebrate the Star Wars movies.