(Recasts, adds Putin quotes, details)

By Dmitry Solovyov

MOSCOW, April 3 (Reuters) - Russian President Vladimir Putin promised increased support for Georgia's breakaway South Ossetia and Abkhazia regions on Thursday after NATO leaders said Georgia would one day be able to join the Western defence alliance.

Putin has repeatedly warned against Georgia's integration with the alliance and, in a letter to the separatists' leaders, he linked Moscow's renewed support for the two rebel regions directly to Tbilisi's bid for NATO membership.

Putin arrived at the NATO summit in Bucharest on Thursday hours after member countries committed to admitting Georgia, though without setting a date.

"(President) Putin shared the concerns of the leaders of Abkhazia and South Ossetia about the likely negative consequences of Georgia's accession to NATO."

"Any attempts to put political, economic or even military pressure on Abkhazia and South Ossetia will not achieve their goals and are counter-productive," Putin wrote in the letter, which was released by the Russian foreign ministry.

"The Russian side intends to further widen and deepen its all-embracing practical cooperation with Abkhazia and South Ossetia for the good of their peoples, in the interests of safeguarding peace, security and stability in the region."

Russia keeps hundreds of its peacekeepers in the two regions and has provided diplomatic and financial assistance to the separatists. The majority of locals hold Russian citizenship.

Tbilisi has accused Moscow of using its influence over the breakaway regions to apply pressure on Georgia's pro-Western leadership.

"The President of the Russian Federation stressed Russia is far from indifferent towards the aspirations and problems of the two republics' populations, of the Russian citizens living there," the Foreign Ministry cited Putin's letter as saying.

"This is why support for Abkhazia and South Ossetia will continue to be not declarative but concrete."

Putin is to be a guest of honour at the NATO summit and take part in a session of the NATO-Russia Council on Friday.

Analysts had earlier predicted Russia would retaliate over closer ties between NATO and Georgia by ramping up support to the separatist regions, though stopping short of recognising them as independent from Georgia.

Russia's State Duma lower house of parliament unanimously adopted a resolution last month urging the Kremlin to consider recognising the independence of Abkhazia and South Ossetia.

The resolution, branded by Tbilisi "barefaced interference" in Georgia's internal affairs, also called for speeding up the recognition if Georgia was put on the track to join NATO.

Moscow has also signalled it could use Kosovo's declaration of independence from Serbia in February -- which it fiercely opposed -- as a precedent to recognise separatists closer to home. (Reporting by Dmitry Solovyov; Editing by Charles Dick)

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