MOSCOW, May 28 (Reuters) - Russian President Vladimir Putin warned the West on Tuesday that NATO members in Europe were playing with fire by proposing to let Ukraine use Western weapons to strike deep inside Russia, which he said could trigger a global conflict.

More than two years into the deadliest land war in Europe since World War Two, Putin has increasingly spoken of the risk of a much broader global conflict as the West grapples with what to do about the advance of Russian troops in Ukraine.

NATO Secretary General Jens Stoltenberg told The Economist that alliance members should let Ukraine strike deep into Russia with Western weapons, a view supported by some NATO members but not by the United States.

"Constant escalation can lead to serious consequences," Putin told reporters in Tashkent. "If these serious consequences occur in Europe, how will the United States behave, bearing in mind our parity in the field of strategic weapons?"

"It's hard to say - do they want a global conflict?"

Putin said Ukrainian strikes on Russia with long-range weapons would need Western satellite, intelligence and military help - so the West would be directly involved. He said sending French troops to Ukraine would be a step towards a global conflict.

Speaking of NATO members in Europe, Putin said that small countries there "should be aware of what they are playing with", as they had small land areas and very dense populations.

"This is a factor that they should keep in mind before talking about striking deep into Russian territory," Putin said.