"I think that out of difficult times opportunities present themselves," Biden said in a joint media appearance with Greek Prime Minister Lucas Papademos in Athens before the two began private meetings.
"And with a lot of hard work and a little bit of luck, a year from now we will have not only weathered this crisis but even be in a stronger position," the vice president said.
Biden said the United States is ready to help any way it can as Greece meets "some very difficult requirements of the [International Monetary Fund] and the European Union" to put the country's financial house in order.
He said it was "overwhelmingly in the interest of the United States" that Greece gets through its financial crisis and remains a strong, vital member of the European Union.
Papademos said he and Biden would have "substantive and productive discussions" on a number of issues, including Cyprus, North Africa, the Balkans, economic relations and the economic measures Greece is taking.
Biden, conducting a diplomatic visit that included visits to Iraq and Turkey, also met with Greek President Karolos Papoulias.
Asked by reporters if he had a message for Europe, Biden replied, "Hang in there."