UPDATE 2-Russia may halt gas transit to Europe by July

* Russia says may stop transit to Europe by early July

* Comments come only 4 months after last gas stoppage

* Finland PM says pipeline decision seen in Sept-Oct

* Putin says timber duties discussion to resume in Sept

(Adds more Putin quotes, Finnish PM on Nord Stream)

By Gleb Bryanski and Brett Young

HELSINKI, June 3 (Reuters) - Russia on Wednesday said it may cut gas supplies to Ukraine at the end of June or in early July if Ukraine does not pay for gas to be pumped into underground storage, once more threatening transit supplies to Europe.

Russia's warnings about gas transit risks send shivers throughout Europe and are often followed by Russian calls to speed up construction of alternative gas export routes bypassing transit countries.

"Gazprom will only supply the gas which has been prepaid. Without the gas pumped into storage, Ukraine will simply not survive and will be forced to take gas destined for transit," Russian Prime Minister Vladimir Putin told a news conference in Helsinki.

"This may lead to a stoppage of gas transit to Europe in the end of June or start of July," Putin said.

Russia, which supplies a quarter of Europe's gas mainly via Ukraine, cut gas to Ukraine twice in recent years due to pricing disputes amid icy political relations between Moscow and Kiev.

The cuts led to serious disruptions of gas supplies to Europe, especially in January 2009, and have strengthened calls in the EU for greater energy supply diversification.

Barely four months after that dispute, Russia rejected a Ukrainian proposal to defer payment on up to $5 billion in gas storage fees. Moscow has urged the European Union to help Kiev pay the bills, but the EU's response has been cool.

TRIGGER LOSSES