MOSCOW, Oct 4 (AFP) - The Kremlin said on Tuesday that it did not want to take part in "nuclear rhetoric" from the West after a media report that Russia was preparing to demonstrate its willingness to use nuclear weapons in its conflict with Ukraine.

The Times newspaper reported on Monday that the NATO military alliance had warned members that President Vladimir Putin was set to demonstrate his willingness to use nuclear weapons by carrying out a nuclear test on Ukraine's border.

The London-based newspaper also said Russia had moved a train thought to be linked to a unit of the defence ministry that was responsible for nuclear munitions.

NATO has not observed changes in Russia's nuclear posture, but is vigilant, an alliance official said on Tuesday, while a Western diplomat, commenting on the Times report, told Reuters that NATO had not warned allies about a nuclear threat from Russia.

When asked about the Times report, Kremlin spokesman Dmitry Peskov said Russia did not want to take part in what he cast as Western exercises in "nuclear rhetoric".

"The Western media, Western politicians and heads of state are engaging in a lot of exercises in nuclear rhetoric right now," Peskov said. "We do not want to take part in this."

Italian daily La Repubblica reported on Sunday that NATO had sent its members an intelligence report on the movements of the Belgorod nuclear submarine.

"Now it is back to dive in the Arctic seas and it is feared that its mission is to test for the first time the super-torpedo Poseidon, often referred to as 'the weapon of the Apocalypse'," La Repubblica said.

The Italian defence minister declined to comment on the matter.

Asked how Britain would respond to the use of "tactical" nuclear weapons by Russia, Britain's foreign minister James Cleverly told a fringe event at the Conservative Party conference that he couldn't go into detail but there would be a response.

"It would inevitably be the case that the use of nuclear weapons by any country anywhere in the world would not go without a response," he said.

"I'm not going to discuss the nature or the threshold."

Tactical nuclear weapons are essentially nuclear weapons used on the battlefield that are much less powerful than the big bombs that would destroy large cities such as Moscow, Washington or London.

Putin on Sept. 21 ordered Russia's first mobilisation of military reservists since World War Two to put more troops on the battlefield and backed a plan to annex swathes of Ukraine, warning the West he was not bluffing when he said he'd be ready to use nuclear weapons to defend Russia.

Russia is the world's biggest nuclear power based on the number of nuclear warheads: It has 5,977 warheads while the United States has 5,428, according to the Federation of American Scientists.