* Talks aim to calm Russian fears over EU-Ukraine trade deal
* EU has rejected proposal for three-way talks in the past
* EU set to sign Ukraine deal on June 27
BRUSSELS, June 13 (Reuters) - The European Union and Russia agreed on Friday to hold high level talks, including Ukraine, on Kiev's expected signing of an EU free trade agreement after Moscow warned last week it would retaliate with measures to protect its economy.
Ukraine's government is set to sign the free trade agreement with the European Union on June 27, over the objections of Russia, which fears the agreement will be harmful for its own economy.
Last November, the EU rejected an idea of trilateral talks with Russia on Ukraine's EU association agreement, a deal that would mark a historic Westwards shift by the former Soviet republic away from Russia's orbit.
The current offer still does not give Russia a say on the shape of Ukraine's agreement, it only opens the way for trilateral consultations on the consequences of the deal.
But it still appears to be a partial concession on the part of the EU to better engage Moscow.
In a phone call to Russian President Vladimir Putin on Friday, European Commission President Jose Manuel Barroso offered to raise the level of consultations with Moscow on the Ukraine agreement to a political, from an expert one, the Commission said in a statement.
"They (Barroso and Putin) discussed the upcoming signature on 27 June of the Association Agreement and the Deep and Comprehensive Free Trade Area with Ukraine," the statement said.
"As a way to dispel any concerns, President Barroso offered President Putin the possibility to pursue the ongoing bilateral talks with Russia at technical level as well as to hold political level consultations, associating Ukraine," it said, adding Putin agreed.
The political level talks may involve EU Trade Commissioner Karel De Gucht and possibly Russia's economy minister, officials said.
Ukraine's association agreement with the EU has been at the heart of the conflict between Moscow and Kiev, which led to the Russian annexation of Crimea in March and the subsequent pro-Russian separatist uprising in eastern Ukraine.
Under intense pressure from Moscow, which wants Ukraine to become part of its own Eurasian union, former Ukrainian President Viktor Yanukovich renounced plans to sign the EU deal last November, just days before the signing ceremony.
The choice of closer ties with Russia rather than the EU triggered popular protests in Ukraine that eventually toppled Yanukovich.
The EU is mediating in separate talks between Russia and Ukraine on a gas pricing dispute. Ukraine began preparing on Friday for Russia to cut off its gas after talks on the dispute broke down, raising the prospect of supplies to the European Union also being disrupted from Monday. (Additional reporting by Adrian Croft; Editing by Alison Williams)