“We do not rule out that the murder has a commissioned character,” he added.
On Saturday President Volodymyr Zelensky said a major police operation was under way.
“All versions are being investigated, including the one that leads to Russia,” he said.
The hardline nationalist Svoboda (Freedom) political party Ms Farion was a member of blamed Russia directly for the killing.
“Moscow shoots in the temple for the Ukrainian language,” it said in a statement.
In 2023, Ms Farion said that true patriots of Ukraine should not speak Russian in any settings, including on the front lines, as it is the language of the aggressor country.
She described Russian as “the language of the enemy, who kills, discriminates, insults and rapes me”, and added: “How crazy should you be to fight in the Ukrainian army and speak Russian?”
Her words provoked a strong reaction in Ukraine at the time, with people accusing her of inciting hatred based on linguistic preferences.
She was dismissed from a university in western Ukraine and was investigated by the Security Service of Ukraine (SBU).
In May, the Lviv Court of Appeal reportedly issued a ruling reinstating her to the position.