By Russian Affairs Analyst, Stephen Dalziel

Chechen rebels say they have withdrawn all their forces from the capital, Grozny, although Russia maintains this is not true.

Russia does claim, though, that the fighting is nearly at an end.

But if the Chechens have withdrawn, it means that they are still going to be able to fight another day.

And acting Russian President Vladimir Putin will be content if that "other day" comes after he has secured victory in the presidential election on 26 March.

The fog of war surrounding Chechnya has become so confused that the Russian side is now denying Chechen claims which, if true, would actually suit the acting Russian President, Vladimir Putin.

The Russian military may simply find it embarrassing to admit that all Chechen fighters have withdrawn from the capital, Grozny, as it would suggest that their encirclement of the shattered city was far from complete.

Russian flag in the centre of Grozny

What is clear is that Russian forces have raised their national flag in Minutka Square in Grozny, a strategically-important road junction leading to what is left of the city centre.

And reports suggest that at least some of the rebels have left Grozny, taking significant casualties on the way.

Chechen officials say that the Mayor of Grozny, Lecha Dudayev - the son of the late Chechen leader, Dzhokhar Dudayev - has been killed.

And, even more importantly, it appears that Shamil Basayev, the Chechens' most feared and respected military commander, may have been seriously wounded.

The overall message in these reports from both sides seems to be good news for Mr Putin.

Mr Putin's presidential chances

All commentators agree that the single biggest threat to Mr Putin's chances of becoming President in the election on 26 March would be if the military operation in Chechnya started to go badly wrong, and Russian casualties increased dramatically.

The Russian military has already admitted that more than a thousand Russian soldiers have been killed - a significant rise in deaths since the assault on Chechnya switched from being largely air and artillery attacks to a ground offensive.

When this increase in casualties was acknowledged, Mr Putin reminded the Russian people that the military campaign was preceded by a series of bomb attacks on apartment blocks in Russian cities, and warned that that danger had not gone away.

For those who believe that it was not Chechen rebels, but the Russian authorities themselves which were behind the bomb attacks, that sounded like a threat aimed at keeping public opinion firmly behind the government.

If the Chechen fighters have withdrawn from Grozny, the Russian media - especially television - will be expected to make much of this over the next few days.

The power of pictures from Grozny

Pictures from Chechnya which show not fighting, but some kind of peace on the streets, will be expected to persuade people that, unpleasant though the military operation has been, it was worthwhile to help bring stability to Russia as a whole.

And, it was carried out by Mr Putin, a Russian leader who has not been afraid to show the toughness which so many Russians seek in those who sit in power in the Kremlin.

If the fighting around Grozny is calming down, Mr Putin's message to his army will be to ensure that they maintain some kind of stability for the next few weeks.

If the rebels have withdrawn to the mountains, he and his military commanders know that they will be back to fight again.

But, for Mr Putin's presidential ambitions, that will matter far less if it is after 26 March.