Many in Ukraine’s Russian-speaking regions oppose his overthrow and the installation of a more European-leaning interim administration.
Russia is also angry at the changes, but Foreign Minister Sergei Lavrov has said Moscow will not intervene.
The formation of a unity government has been delayed until Thursday.
Addressing parliament, Oleksandr Turchynov said he would meet law enforcement agencies to discuss the risk of separatism in regions with large ethnic Russian populations.
Separatism was a “serious threat”, he said.
Crimea and some pro-Russian areas in the east have seen protests against the overthrow of Viktor Yanukovych, sparking fears of secession.
The delay in announcing a unity government was to allow further consultations, Oleksandr Turchynov said, adding that “a coalition of national faith must be elected”.
Russia has been vehemently opposed to the changes in Ukraine, with PM Dmitry Medvedev saying on Monday that those behind the new administration had conducted an “armed mutiny”.
At a news conference in Moscow on Tuesday, Sergei Lavrov warned other states against seeking “unilateral advantages” in Ukraine, but said Russia’s “policy of non-intervention” would continue.
“It is dangerous and counter-productive to try to force on Ukraine a choice according to the principle of either being with us or against us,” he said.
Sergei Lavrov added that “it is in our interest for Ukraine to be part of the broad European family” but against Russia’s interest to “allow the radicals and nationalists who are clearly trying to take centre stage to prevail.”
It is still unclear where Viktor Yanukovych is, but an arrest warrant has been issued. He was last reportedly seen on Sunday in Balaklava on the Crimean peninsula.
Acting Interior Minister Arsen Avakov said a criminal case had been opened against the ousted president and other officials over “mass murder of peaceful citizens”.
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