BRUSSELS - NATO chief Anders Fogh Rasmussen hopes to secure Russian help in equipping and training Afghan security forces during a visit to Moscow in December, an alliance spokesman said on Wednesday.

Rasmussen will meet President Dmitry Medvedev, Prime Minister Vladimir Putin and the foreign and defense ministers during the December 15-17 visit, his first to Moscow since taking over as the defense alliance's secretary-general on Aug 1.

NATO spokesman James Appathurai said there was a possibility Moscow could also agree to broaden agreements on the transit of NATO supplies to Afghanistan through Russia.

On Afghanistan there is a clear prospect of stepping up cooperation and it is supported by a clear shared interest, Appathurai told reporters.

Russia has no more desire to see terrorism, extremism and drugs flow out of Afghanistan than any of us, he said.

Appathurai said that although NATO was seeking better ties with Russia, they would not come at the expense of promises the alliance has made to the former Soviet republics of Ukraine and Georgia that they can one day join the alliance.

There will be no compromise on core principles, but a strong push to expand practical cooperation, Appathurai said.

NATO froze relations with its former Cold War foe after last year's war between Georgia and Russia but they have started to warm again.

Moscow has said it backs U.S.-led efforts against an Islamist insurgency in Afghanistan but that it will not send its own soldiers back to the country where it fought a war in the 1980s.

NATO wants to beef up the Afghan police and army before withdrawing Western forces that were sent to Afghanistan after the attacks on the United States on September 11, 2001.

There are more than 100,000 foreign troops in the country, but they have struggled to contain the widening insurgency and mounting casualties have made the mission increasingly unpopular with Western public opinion.

(Editing by Elizabeth Fullerton)