De Hoop Scheffer, speaking after talks with Russian President Vladimir Putin in Moscow, also urged both sides to show restraint and ease tensions.
And he called on Russia not to link current tensions with Tbilisi with NATO's recent decision to launch an "Intensified Dialogue" with Georgia.
Putin, in a televised appearance on October 25, accused Georgia's government of seeking to use military force to resolve conflicts in its breakaway regions of South Ossetia and Abkhazia. Earlier today, Putin praised Russia's "successful" cooperation with the alliance.
"We continue [NATO-Russia] cooperation in assisting NATO countries in Afghanistan, we have now joined your work in the Mediterranean Sea, our Emergency Situations Ministry is cooperatting [with NATO] on emergency response planning," Putin said. "I would also like to note our political dialogue, which is maintained constantly and at the highest level."
De Hoop Scheffer said Russia's involvement was necessary for the solution of many international conflicts.
Foreign Minister Sergei Lavrov earlier this week said in talks with de Hoop Scheffer that Russian officials will raise Moscow's concerns over NATO's eastward expansion and U.S. plans to deploy missile-defense sites in Eastern Europe.
Deputy Foreign Minister Aleksandr Grushko said NATO's recent decision to launch an Intensified Dialogue with Georgia, which aspires to join the alliance, has prompted Georgia's government to "provoke" Moscow.
(compiled from agency reports)