Washington led a push for the alliance to allow them in through a so-called Membership Action Plan, or MAP.
Britain has proposed investigating other ways to bring them into the alliance, Rice says.
Moscow strongly opposes giving Nato membership to Georgia and Ukraine, saying that Russia's security would be threatened if the two neighbours join the alliance.
Medvedev was in Havana to discuss energy, military and trade deals, having already visited Venezuela, itself a member of the Organisation of Petroleum Exporting Countries (Opec).
Raul Castro, Cuba's president, and Medvedev held talks on the global financial crisis and economic and military ties.
"We have a systematic dialogue. Our relations have been generally good, but in the past six months they have become especially intense," Medvedev told reporters after meeting with Castro.
Medvedev is the first Russian leader to visit Havana since Vladimir Putin, then president, closed down Russia's Lourdes intelligence base in 2001.
The closure of the base led to a souring of relations between the countries and the visit by Medvedev appears aimed at improving the bilateral relationship.
While Havana is looking diversify its trading partnerships, Russia is thought to be looking for new markets so that it can ride out the worldwide financial crisis.
The trip to the Cuban capital comes amid tensions between Moscow and Washington over Russia's war with Georgia in August and US plans for a missile defence shield.
Moscow has said that Washington should abandon its economic embargo of Cuba, which was imposed in 1962, three years after Fidel Castro took power in an armed revolution.
Havana received economic and military support from Moscow during the Cold War but the 1991 collapse of the Soviet Union badly damaged Cuba's economy.