UPDATE 2-Many Ukrainian fighters remain in Azovstal, commander says operation going on

* Unknown number of fighters still in steel works

* Russia says over 1,700 have already surrendered

* Azov Regiment deputy commander cites operation going on

* Red Cross issues reminder about treatment of prisoners of war (Adds deputy commander of Azov regiment releasing video)

By Guy Faulconbridge

LONDON, May 19 (Reuters) - Russia's siege of the Ukrainian city of Mariupol stuttered towards its end on Thursday, with hundreds of fighters still holed up in the Azovstal steel works and some 1,700 who have already surrendered facing an uncertain fate.

A full abandonment of the bunkers and tunnels of the bombed-out plant would end the most destructive siege of a war that began when Russia invaded Ukraine on Feb. 24.

It was unclear how many fighters remained inside.

Russia's defence ministry said 771 fighters from the Azov Regiment had surrendered in the past day, bringing the total of those who had given themselves up since Monday to 1,730.

Ukrainian officials declined to comment, saying it could endanger rescue efforts.

Sviatoslav Palamar, deputy head of the Azov Regiment, released an 18-second video address on Thursday to say he and other commanders were still on the territory of the plant.

"A certain operation is going on, the details of which I will not disclose. Thank you to the whole world and thank you to Ukraine for (your) support," he said.

Denis Pushilin, head of the Russian-backed separatist Donetsk People's Republic, which now encompasses Mariupol, said more than half the fighters had surrendered, and that the uninjured had been taken to a penal colony near Russian-controlled Donetsk.

"Let them surrender, let them live, let them honestly face the charges for all their crimes," he told an online video channel.

Russia needs Mariupol, one of Ukraine's main seaports, to cement its control of land it has seized along the coast, reaching all the way west to annexed Crimea.

The city is now an urban wasteland shattered by artillery and street-by-street fighting.

Before the war its population was around 430,000. Pushilin said 200,000 remained, although Ukrainian officials have said it is only half that number.

GENEVA CONVENTIONS

Ukrainian President Volodymyr Zelenskiy says Mariupol's last defenders - regular soldiers as well as members of the National Guard, to which the Azov Regiment belongs - are national heroes, and that he hopes they can be exchanged for Russian prisoners.

Moscow portrays the regiment as one of the main perpetrators of the alleged radical anti-Russian nationalism and neo-Nazism which it says threaten Ukraine's Russian-speakers.

The unit, formed in 2014 as a militia to fight Russian-backed separatists, denies being fascist, racist or neo-Nazi, and Ukraine says it has been reformed away from its radical nationalist origins.

The Kremlin said the combatants would be treated in line with international norms, though some Russian lawmakers demanded they be tried for war crimes and one demanded they face the death penalty.

The Swiss-based International Committee of the Red Cross (ICRC) said it had registered those leaving the plant to keep track of prisoners.

It also explicitly set out the rules of the 1949 Geneva Conventions, the body of international law relating to the treatment of captured military personnel and civilians.

"The ICRC must have immediate access to all POWs in all places where they are held," it said. "The ICRC must be allowed to interview prisoners of war without witnesses."

(Reporting by Guy Faulconbridge; additional reporting by David Ljunggren; editing by Kevin Liffey and Jonathan Oatis)