By David Brunnstrom

BRUSSELS, Dec 19 (Reuters) - Russia said on Friday it was heading towards normalisation of relations with NATO after its first high-level contact with the alliance since a suspension of such ties following Moscow's August intervention into Georgia.

But after meeting NATO Secretary-General Jaap de Hoop Scheffer, Russia's NATO envoy Dmitry Rogozin said it would take time to rebuild trust and that reconstructing the relationship would require thorough analysis of the Georgian conflict.

The two sides agreed their lunch in Brussels should be followed in mid-January by an informal session of the ambassador-level NATO-Russia Council, whose meetings NATO suspended to protest against what it called Russia's "disproportionate" use of force against Georgia.

Georgia has been promised eventual NATO membership.

NATO spokeswoman Carmen Romero said Friday's meeting took place in an "excellent atmosphere", while Rogozin told a news conference: "We are heading towards normalisation of our relations and I am very glad about this."

However, Rogozin said rebuilding the relationship would take time. "We are only at the beginning of our very difficult route towards restoring trust."

He said Russia and NATO had common interests in working together on Afghanistan, against piracy, terrorism, drug trafficking and organised crime.

"But we need to build a bridge from August to January ... so we insist on a close and thorough analysis of the aggressive actions taken by the regime of (Georgian President Mikheil) Saakashvili and the reaction of major actors," he said.

Despite their alarm at Russia's invasion of Georgia, NATO's 26 members agreed this month to resume gradually political contacts with Moscow, with European allies arguing that the freeze in ties was counter to the alliance's security interests.

But the allies also reaffirmed a pledge -- which has greatly angered Russia -- that former Soviet states Georgia and Ukraine would one day join the alliance and pledged to step up help to them in that process.

Russia has repeatedly said it does not want a new Cold War and says it intervened in Georgia in response to aggression.

The United States has insisted that resuming high-level NATO contacts with Russia did not mean "business as usual".

On Thursday, U.S. ambassador to NATO Kurt Volker said the United States sought a cooperative relationship with Russia. "But we want Russia to act as a modern 21st century partner for NATO," he said. (Editing by Philippa Fletcher)

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