Speaking at an investment forum in St Petersburg, Putin said Russia would "respect the choice of the Ukrainian people" and would work with the new leadership.
He said he was upbeat on the prospects for resolving the crisis in Ukraine and that doing so would help improve relations with the United States.
"I'm an optimist. I am not losing faith that the situation in Ukraine will at some point become normal and we will find the inner strength to normalize relations (with the United States)," Reuters reported.
He also said that Russia did not want to isolate itself from the rest of the world and that it wanted to work with the United States on many projects.
"We are not planning any self-isolation," Putin said. "We hope that common sense ... will prompt our European and US partners to work with Russia,"
Russia will also pull back all forces deployed to regions near its border with Ukraine "within a few days," a deputy defence minister said on Friday, a move that if carried out could assist to ease tensions.
Moscow has concentrated tens of thousands of troops across the border from eastern Ukraine, where pro-Russian separatists have declared two independent states.