The two-day round of talks began on Monday in Riyadh, Saudi Arabia's capital. Six rounds of bilateral consultations have been held between the countries since May 2007.
A source in the Russian delegation said: "During the visit, the Russian delegation plans to make as much progress as possible at bilateral talks with Saudi Arabia. We aim to resolve outstanding issues, and it is possible that final agreements will be reached in Riyadh."
Russia, the largest economy outside the WTO, has been seeking membership in the organization since 1993. So far, Moscow has concluded bilateral talks with over 60 states, but still needs to complete discussions with two WTO members - Saudi Arabia and Georgia.
Saudi Arabia, the world's largest oil producer, had to raise domestic oil prices to global levels before joining the trade body in 2005, and is now making similar demands on Russia.
The agenda for the talks on Tuesday will include Russia's market for goods and services.
Earlier, the sides reached agreements on agriculture, the protection of geographic and religious names, and on manufactured goods.
"The service sector issues that are still open relate to credit, finance and energy," the source said.
He said that "one or two issues" may remain unresolved, but can be overcome in the nearest future.
On Monday, Russian Prime Minister Vladimir Putin held a telephone conversation with Saudi Arabia's King Abdullah to discuss Russia's plans for accession to the WTO.
