Parliament had earlier voted to seize the Kiev luxury estate of ousted Yanukonych whose whereabouts is currently not known.
The speaker said in Parliament they had a task of forming a new unity government in attempt to resolve the chaotic situation in the country.
While Yanukovych has described the decision to vote him out as as a coup, thousands of opposition protestors remain at the Independence Square where the situation is said to be calm.
About 88 people, mostly protesters, are now known to have been killed in clashes since 18 February, health minister has said.
Mr Turchynov, a close associate of Ms Tymoshenko, described forming a unity government as a “priority task”.