Mykola Azarov said Moscow had offered to hold trilateral talks on the issue, without giving “any ultimatums”.
Kiev last week put on hold the association and free trade deal with the EU, prompting Brussels to accuse Moscow of exerting pressure on Ukraine.
The move triggered huge pro-EU protests in Kiev and other Ukrainian cities.
Russian President Vladimir Putin has denied putting any pressure on Kiev, accusing instead the EU of “blackmailing” Ukraine into signing the agreement.
Speaking to reporters in Kiev on Tuesday, Mykola Azarov acknowledged that Russia had suggested “to delay signing the treaty and to conduct negotiations” between Kiev, Moscow and the EU.
He said Ukrainian President Viktor Yanukovych would still attend this week’s EU summit in Vilnius, Lithuania, to discuss the possible consultations with Brussels and Moscow.
It had been originally planned that Ukraine would sign the treaty with the EU at the 28-29 November summit.
Mykola Azarov said such three-way talks would be in the best interests of Ukraine: “We absolutely do not want to be a battlefield between the EU and Russia. We want to have good relations with both the EU and Russia.”
He also added that separate “road-map” talks with Russia aimed at reviving economic ties would start next month and no agreement had been finalized on possible new financial support from the Kremlin.
Meanwhile, President Putin said it was solely up to Ukraine whether to sign or not the agreement with the EU.
During a visit to Italy, Vladimir Putin also urged EU leaders to refrain from “sharp words” on the issue.
Ukraine’s government said last Thursday it was halting preparations for signing the deal with the EU, amid concerns this would have a negative impact on Kiev’s trade relations with Russia and cause mass job losses as a result.
Moscow had earlier warned it would be forced to defend its market by raising custom duties on Ukrainian goods.
In a statement on Monday, Viktor Yanukovych said he had been forced to halt treaty preparations by economic necessity and the desire to protect those “most vulnerable”.
Tens of thousands of protesters have been taking to the streets of Ukraine’s major cities since last week.
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