* Moscow and Kiev say leaders find common ground
* Confusion after Kiev speaks of ceasefire
* Obama in Estonia on eve of NATO summit
* Russian announces exercise by nuclear forces
By Gareth Jones and Mark Trevelyan
KIEV/MOSCOW, Sept 3 (Reuters) - Ukraine said on Wednesday its president had agreed with Russia's Vladimir Putin on steps towards a "ceasefire regime" in Kiev's conflict with pro-Russian rebels, but the Kremlin denied any actual truce deal, sowing confusion on the eve of a NATO summit.
"The parties reached mutual understanding on the steps that will facilitate the establishment of peace," said a statement by Ukrainian President Petro Poroshenko's office, replacing an earlier statement that had spoken of a "permanent ceasefire".
Putin's spokesman said the leaders agreed on steps towards peace but not a ceasefire in the conflict, which has killed more than 2,600 people since April and provoked the worst crisis in relations between Russia and the West since the Cold War.
"Putin and Poroshenko really discussed the steps that would contribute to a ceasefire between the militia and the Ukrainian forces. Russia cannot physically agree to a ceasefire because it is not a party to the conflict," spokesman Dmitry Peskov said.
That position is disputed by Kiev and Western governments, which say Russian troops are fighting alongside the pro-Moscow separatists.
Despite the confusion, the statements appeared to indicate a degree of progress that could influence European Union leaders as they consider introducing new sanctions against Russia as early as Friday.
In a contradictory signal, Moscow simultaneously announced plans for huge military exercises this month by the strategic rocket forces responsible for its long-range nuclear weapons. It said the manoeuvres in south-central Russia would involve 4,000 troops and extensive use of air power.
The timing was clearly calculated to throw down a challenge to NATO and the United States, hours before President Barack Obama was due to deliver a speech (1200 GMT) on the crisis in Russia's neighbour Estonia.
Obama was expected to affirm the commitment of the United States and NATO to defend its members in Eastern Europe in the face of what they see as Cold War-style Russian aggression.
Russia denies any military presence in Ukraine, despite what Western governments have called overwhelming evidence that it has sent in troops and tanks to rescue the separatists from defeat and enable them to turn the tide of the conflict.
"You want to talk provocative? Let's talk about a few thousand Russian troops inside eastern Ukraine, continuing to support separatists, with heavy weapon systems, and more than 10,000 troops arrayed along the southeast border with Ukraine," Pentagon spokesman Rear Admiral John Kirby said on Tuesday.
When he met Poroshenko in Belarus eight days ago, Putin had said Russia would help to facilitate peace moves, but the actual agreement of a ceasefire would be an internal matter for the Ukrainian government and the rebels.
Initial reaction from the rebel side appeared sceptical towards the possibility of any breakthrough.
A senior rebel leader said the separatists were sticking to their demand for Ukrainian troops to withdraw from "our territory" as the main condition for peace. (Additional reporting by Gabriela Baczynska in Donetsk and Lidia Kelly and Jason Bush in Moscow; Writing by Mark Trevelyan; Editing by Will Waterman)