BUDAPEST, Oct 9 (Reuters) - The United States is pushing NATO to put Georgia on a formal track to alliance membership in December, U.S. Defense Secretary Robert Gates said on Thursday, despite concerns about the country's security after its war with Russia.

NATO has promised to grant both Georgia and Ukraine membership eventually but declined in April to give either a formal membership action plan, known as MAP.

"I urge our allies to support MAP for Georgia in December and to support Georgia's efforts in accomplishing needed reforms," Gates told reporters on the sidelines of a NATO defence ministers' meeting in Budapest.

Following the Georgia-Russia conflict in August, some allies want to delay extending NATO membership to either Georgia or Ukraine, according to U.S. officials.

But Washington has been at pains to show that Russian actions will not change U.S. policy and U.S. officials say it should not affect NATO policy either.

"We are unwavering in our support for Georgia's sovereignty, its independence and its territorial integrity," Gates said.

"We have sought a constructive relationship with Russia, but unfortunately their behavior has undermined security in the region and raised real concerns about their intentions. Russia's invasion of Georgia in my view has achieved, will achieve no strategic objective."

The conflict started in early August when Georgian troops tried to retake by force a separatist, pro-Moscow region that threw off Georgian rule in the 1990s. Russia responded with a counterstrike and sent troops deep into Georgia's heartland, drawing international condemnation.

NATO has frozen ties with Moscow in response.

U.S. and Georgian officials will meet in late October to talk about how Washington can help rebuild the Georgian military. Gates and Georgian Defence Minister David Kezerashvili met in Budapest but did not discuss specific weapons systems that Georgia might need. (Reporting by Kristin Roberts, Editing by Angus MacSwan)

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