The interim leader said intervening on the south-eastern Black Sea peninsula, where Kremlin-backed forces have seized control, would leave Ukraine exposed on its eastern border, where he said Russia has massed "significant tank units".
"We cannot launch a military operation in Crimea, as we would expose the eastern border and Ukraine would not be protected," Oleksandr Turchynov told Agence France-Presse.
"They're provoking us to have a pretext to intervene on the Ukrainian mainland … [but] we cannot follow the scenario written by the Kremlin."
Crimea is due to hold a referendum on joining Russia this Sunday, organised by the peninsula's self-appointed leaders.
Turchynov described the secession referendum as a sham whose outcome would be decided "in the offices of the Kremlin".
The European Union is poised to impose travel bans and to freeze the assets of Russian officials and military officers involved in the occupation of Crimea by next Monday if Moscow declines to accept the formation of a "contact group" to establish a dialogue with Ukraine.
But Russian leaders are currently refusing to communicate with Ukraine and refuse to accept Turchynov's legitimacy.
"Unfortunately, for now Russia is rejecting a diplomatic solution to the conflict," he said.
A meeting of EU foreign ministers in Brussels on Monday is being seen as an unofficial deadline for the introduction of the sanctions, which would exempt the Russian president, Vladimir Putin, and his foreign minister, Sergei Lavrov, as the EU tries to keep open lines of communication.
Ukraine's parliament warned the regional assembly in Crimea on Tuesday that it faces dissolution unless it cancels the referendum, which has been condemned by the EU and the US as illegal.
But the Russian foreign ministry said it would respect the result of the vote.
On Wednesday, a Russian court issued an arrest warrant for Ukrainian far-right leader Dmytro Yarosh in absentia on charges of inciting terrorism – a symbolic move in support of Moscow's argument that "extremists" stole power in neighbouring Ukraine.
Russian news agencies said Moscow's Basmanny district court ruled that Yarosh – one of the most influential leaders of the protest movement which ousted former Ukrainian president Viktor Yanukovich – should be arrested for making "public calls for terrorist and extremist activities via the media".
Ukraine's new justice authorities have issued warrants for the arrest of pro-Russia leaders in the Crimea region.
EU sanctions against Moscow are what leaders describe as phase II of a three-stage plan that would involve curbs on energy, trade and financial relations if Russian forces move beyond Crimea to the main part of eastern Ukraine.
David Cameron's spokesman said: "The prime minister is very much linking phase II to the need for dialogue to start in the next few days. We are asking [the officials] to do preparatory work and we still believe there is an opportunity for the dialogue to start and we very much encourage the Russian authorities to start that.
"The focus [of the sanctions will] be on officials who are closely linked to infringements on Ukrainian sovereignty."
Source: The Guardian