Biden held nine phone calls with ousted Ukrainian leader Viktor Yanukovych in recent weeks, seeking to quell political violence, and has emerged as the White House's top pointman on the issue.
Biden and Burkhalter "consulted on the current situation in Ukraine, including what support the United States and the OSCE could offer to help return the country to peace and stability, to ensure justice and accountability, and to strengthen democratic institutions as Ukrainians chart their future course," a White House statement said.
The 57-nation Organization for Security and Cooperation in Europe (OSCE) is seeking to act as a coordinator of aid and assistance to the transitional government in Kiev.
The OSCE, headquartered in Austria, operates by consensus and counts countries from Europe, North America and Central Asia -- including Ukraine but not the United States -- as members.
Switzerland currently holds the rotating chairmanship of the OSCE.
Biden also thanked Burkhalter for Switzerland's role in representing US diplomatic interests in countries where it has no diplomatic relations, including Iran and Cuba.
Burkhalter, who holds the Swiss presidency, which rotates yearly among a seven-member cross party cabinet, also discussed the threat of violent extremism, non proliferation and humanitarian assistance with Biden at the White House meeting, the statement said.