Writing on social media, Bildt says: "Everyone in Ukraine has a responsibility to secure a peaceful and non-violent solution after the tragic deaths of this day."
He later added: "Everyone has responsibility to take country back from brink of catastrophe."
The demonstrations in Kiev started in November last year, initially as a protest against a trade deal with Russia.
Bildt visited Kiev in early December for talks with both sides of the conflict. He also met with demonstrators on Independence Square in the centre of the city.