Duterte's remarks came a day after Russia's ambassador said his country was ready to supply the Philippines with sophisticated weapons and aims to become its close friend.
"We welcome our Russian friends. Anytime you want to dock here for anything, for play, for replenish supplies or maybe our ally to protect us," Reuters quoted Duterte as saying in a meeting with Rear Admiral Eduard Mikhailov, head of the Flotilla of the Russian Navy Pacific Fleet.
Duterte has thrown the future of Philippine-US relations into question with angry outbursts against the US and some scaling back of military ties while taking steps to improve relations with China and Russia.
Duterte is due to go to Moscow in April.
The visit by the Russian warships was the first official navy-to-navy contact between the two countries.