Burkalter currently holds the rotating presidency of the 57-state Organization for Security and Cooperation in Europe (OSCE).
"I met (Ukrainian) Prime Minister (Mykola) Azarov on Friday in Davos in my capacity as OSCE head," Swiss President Didier Burkhalter told reporters in Warsaw at a joint press conference with Polish counterpart Bronislaw Komorowski.
"I told him about our availability and several concrete proposals for action to improve the chances of dialogue and decrease the risk of violence," he said, adding that "we are waiting for his answer."
Ukraine plunged into its two-month political crisis after President Viktor Yanukovych suddenly refused in November to sign a landmark political and trade deal with the European Union that was years in the making.
He turned instead to the country's former master Russia, infuriating pro-EU Ukrainians.
A Ukrainian government minister warned Monday that a state of emergency could be imposed to deal with the crisis that officials said have left three activists dead.
Switzerland, which is not a member of the European Union, assumed the rotating chairmanship of the OSCE on January 1st.
Geneva facilitated talks between Iran and world powers, which resulted in November's landmark six-month accord aimed at curbing Tehran's controversial nuclear programme.
Since last week Switzerland has also played host to UN-sponsored peace talks between Syria's government and opposition.