The resolution, which is not legally binding, reads that, "the United States should take the lead in supporting the awarding of a Membership Action Plan to Georgia and Ukraine as soon as possible."
It also stated that "a stronger, deeper relationship among the Government of Georgia, the Government of Ukraine, and NATO will be mutually beneficial to those countries and to NATO member states."
Ukraine and Georgia have formally requested to join MAP, a program that prepares countries for accession to the Western military alliance but does not guarantee membership.
U.S. President George Bush arrived in Ukraine late on Monday and following a meeting with President Yushchenko on Tuesday told journalists that, "I'm going to work as hard as I can to see to it that Georgia and Ukraine are accepted into MAP."
Russia is concerned over the membership bids of the former Soviet republics. State Duma Speaker Boris Gryzlov said, "NATO's approach to Russia's borders is a situation that is unacceptable to us, and we will do all we can to prevent that from happening."
"I will continue to make America's position clear: we support the MAP for Ukraine and Georgia," Bush also said.
Bush now heads to a NATO summit in Bucharest on April 2-4. He is then due to meet Russian President Vladimir Putin in the Russian Black Sea resort of Sochi on April 6 for more talks on NATO's expansion and U.S. plans for a missile shield in Central Europe.
Bush reiterated that Ukraine and Georgia's NATO bids were no reason for Russia to be concerned, adding however that, "Russia will not have a veto over what happens in Bucharest."