Bush's plane made a brief refueling stop at the Vnukovo-2 airport ahead of the Pacific Rim countries' summit in Hanoi, Vietnam.
Alexei Gromov said the two leaders confirmed that a bilateral protocol on Russia's accession to the World Trade Organization is being prepared for signing in Hanoi.
The U.S. has agreed to sign a bilateral protocol opening the way for Russia to become a WTO member. The countries' presidents are expected to sign the document on the sidelines of the Asia-Pacific Economic Cooperation (APEC) summit in Hanoi November 19.
Presidential aide Sergei Prikhodko said Putin praised the U.S. agreement to sign the document following lengthy disputes over access to Russia's financial system and U.S. meat imports.
"This means that they have the political will to promote trade and economic and political ties with Russia. It is a tribute to Bush and the U.S. leadership," he said.
The Russia-U.S. bilateral protocol will end six years of Russia's negotiations on WTO accession. Russia, the largest economy outside the 150-nation alliance, has yet to sign bilateral agreements with Sri Lanka and the former Soviet republics of Moldova and Georgia, which have troubled relations with Moscow.