* 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 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.
Under the terms of the supply deal clinched in January, Ukraine is to complete payment for monthly imports by the seventh day of the following month.
No disruption in the payment timetable has so far been recorded, and Ukrainian state energy firm Naftogaz said on Monday it would pay for May's imports in full and on time.
Earlier, the chief of Russian gas giant Gazprom voiced concern about Ukraine's ability to pay.
Gazprom needs to store gas in Ukraine because the capacity of the transit system does not allow it to serve Europe's needs in full during a cold winter without additional gas use from Ukraine's underground storage.
Gas needs to be pumped into storage during the summer when demand in Europe is low, but Gazprom says it cannot simply store it in Ukraine because it is afraid Kiev will misappropriate it.
Gazprom has therefore been selling it to Kiev in recent years and buying it back in winter - a scheme which works well when gas prices are on the rise but which would trigger heavy losses at Naftogaz this year because gas prices are set to fall.
NO REASON NOT TO AUTHORISE
Putin also said he saw no reason why Finland should not authorise the alternative Nord Stream Baltic Sea gas pipeline which will go through Finland's territorial waters and pump 55 billion cubic metres of Russian gas annually to Europe.
"The project does not undermine Finland's interests at all," Putin said. Finland's Prime Minister Matti Vanhanen said three permissions were still needed, with the government's decision expected in September-October.
Permits to build and operate the pipeline are needed from Russia, Finland, Sweden, Denmark and Germany, whose territory it would traverse. Estonia, Latvia, Lithuania and Poland are considered "affected countries" and must be kept informed.
Putin responded by saying that Russia and Finland will discuss a rise in export duties for Russian timber -- a sensitive issue in Finland whose wood processing industry depends on Russian timber -- also in September.
"I would like to remind that at Finland's request a planned hike in export duties for raw timber had been frozen... We hope it will be a two-way street," Putin said. Russia says it hikes the duties to develop its own wood processing industry.
The dispute over the timber duties, set to rise to a prohibitive level next year, is one of the few remaining issues in Russia's 15-year bid to join the World Trade Organisation, which, Putin said, remains Russia's goal. (Reporting by Gleb Bryanski and Brett Young; Editing by Keiron Henderson)