KYIV, March 28 (Reuters) - Russian forces are still edging forward in the bombed-out eastern Ukrainian city of Bakhmut, a Moscow-installed official said on Tuesday (Mar 28), but British intelligence said a Russian tank division had taken heavy losses in the nearby town of Avdiivka.

The battle for Bakhmut, a mining city in the Donetsk region, has been the focus of Moscow's war in Ukraine for months, with both sides describing the fighting there as a "meat grinder".

Denis Pushilin, the Russian-installed leader of the part of Donetsk region under Moscow's control, said most Ukrainian forces had pulled back from the AZOM metals factory on the western side of the Bakhmutka river in the city.

"The important thing here was to clear out the industrial zone at the plant itself. You can practically say that has now been done, with the guys just finishing off (Ukrainian) fighters there who are only left in solitary groups," Pushilin told Russian state TV.

His claims ran counter to Ukrainian and Western assertions that the situation in Bakhmut is stabilising and that Russia's winter offensive is faltering.

In its evening briefing note on Tuesday, Ukraine's military command said Russia continued to conduct assaults in Bakhmut but Ukrainian forces were standing firm and repelling attacks.

Ukraine's eastern command spokesman Serhiy Cherevaty separately said the situation around Bakhmut remained "dynamic".

Ukrainian military commanders have said their own counteroffensive - backed by newly-delivered Western hardware, including German Leopard 2 tanks - is not far off, but have stressed the importance of holding Bakhmut in the meantime.

Russian forces have also been shelling Avdiivka, 90km south of Bakhmut. Many civilians have now been evacuated.

In its daily update on the war in Ukraine on Tuesday, Britain's defence ministry said Russian forces had made only "marginal progress" in an attempt to encircle Avdiivka in recent days and had lost many armoured vehicles and tanks.

Russia's 10th Tank Regiment, taking part in the Avdiivka operation, was dogged by problems of ill discipline and poor morale, and had "likely lost a large proportion of its tanks", the ministry said.

In another sign of the pressure Moscow is facing, Russia said on Tuesday it had for the first time shot down a US-supplied GLSDB guided smart bomb fired by Ukrainian forces.

The Ground-launched Small Diameter Bomb, long sought by Kyiv to hit Russian command centres and supply lines, could double Ukraine's battlefield firing range.

Separately, Ukrainian forces reported repelling 62 Russian assaults along the eastern front over the past 24 hours.

Reuters could not verify the battlefield reports.

Russian-installed officials in Donetsk city said Ukrainian forces killed two civilians late on Monday when they shelled an apartment building there. Reuters reporters saw rescuers combing through the rubble of the building, the lower part of which had collapsed, and one victim's legs protruding from the debris.

There was no immediate comment from Ukrainian authorities.