By Andrew Osborn

MOSCOW (Reuters) - Thousands of Russians marched through Moscow to honor slain Kremlin critic Boris Nemtsov on Saturday, the first anniversary of his death, and to press their demand that the authorities find and punish the person who ordered his killing.

The 55-year-old Nemtsov, an opposition leader and former deputy prime minister, was gunned down near the Kremlin walls late in the evening of Feb. 27, 2015, as he walked home with his girlfriend from a restaurant.

Investigators have charged a group of Chechen men with his murder. But Nemtsov's supporters say the suspects are just low-level operatives who were paid to kill the prominent critic of President Vladimir Putin. They say the person who ordered the hit has been neither identified nor arrested.

"Nemtsov was killed because he had exposed Putin for what he was in various reports," one of the marchers, Irina Vorobyova, 60, told Reuters. "He was a worthy political opponent for Putin but he had insulted him."

Vorobyova, like many on the march, said she thought Ramzan Kadyrov, the Kremlin-backed leader of Chechnya, had ordered Nemtsov's murder to please Putin. Kadyrov denies any involvement, though he has praised one of the suspects as "a true patriot of Russia".

The authorities locked down central Moscow for Saturday's event, sealing in the marchers with metal fencing guarded by police, some of whom wore body armor and helmets.

Police put the number of attendees at 7,500 people, but one group of observers put it at 25,000. Some opposition figures said up to 100,000 people had turned up.

A Reuters reporter saw one man being dragged away into a side street in handcuffs.

"RUSSIA WITHOUT PUTIN"

"Killed for the truth," read one banner. Another, which showed the cross-hairs of a sniper's gun, asked: "Who is next?"

Some carried portraits of Nemtsov and chanted "Russia will be free" and "Russia without Putin". Similar events were staged in other towns across Russia.

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Nemtsov had authored an excoriating report on Putin's rule and, shortly before he was killed, had been working on a report examining the Russian military's role in Ukraine.

Though revered by his supporters as an unpretentious man of the people, some Russians disliked him, associating him with the 1990s, an era of political turmoil and painful reforms, when he served in the government of then-President Boris Yeltsin.

The authorities forbade the marchers from passing the spot where he was killed, on a bridge near the Kremlin. But many went there after the march to lay flowers at an improvised memorial that the authorities have repeatedly tried to destroy.

Opposition-minded Russians accuse the Kremlin of waging a campaign to erase Nemtsov's memory.

The Kremlin has downplayed Nemtsov's significance, calling his murder a "provocation".

Nemtsov's daughter Zhanna has repeatedly said she wants Chechnya's Kadyrov to be questioned about her father's murder.

Kadyrov, who calls himself "Putin's foot soldier", told state-controlled NTV on Saturday: "Nemtsov did not bother me in real life because he was not on my level."

(Writing by Andrew Osborn and Polina Devitt; Editing by Gareth Jones)