EU foreign ministers were urged to consider possible new sanctions against Russia, which is seen as responsible for the latest aggression, when they meet at an emergency meeting on Thursday. A final decision on extra sanctions is not expected to be taken until next month when current sanctions, which were imposed in March 2014, hitting the Russian economy hard, expire.
Read MoreNew Greek finance minister: First goal to 'end the vicious cycle'
Following the EU leaders' statement, however, the new Greek government, led by Prime Minister Alexis Tsipras, complained to EU foreign policy chief Federica Mogherini, saying that the statement did not have their consent.
The move highlights the gap between Greece's new government – which is led by the radical-left Syriza party – and its European partners, and indicates that their differences could go beyond domestic economic policy and austerity measures.
Tsipras, who heads up the anti-austerity party, wants to pare back the cuts imposed on Greece, despite them being a condition of its 240 billion euro ($272 billion) bailout package. After only one day in power, Tsipras halted the sale of the government's stake in the Port of Piraeus on Tuesday. Privatizing public assets was a part of Greece's bailout program.
In addition, Tsipras' government has called on the so-called troika -- the European Central Bank, European Commission and International Monetary Fund -- to write off a third of the country's debt - something euro zone leaders have refused point-blank to consider.
Read MoreNobel winner: Germany's the problem, not Greece
Greece's apparent support of Russia has not only entrenched its apparent collision course with European leaders, but shows it could also be looking to cosy up with the country. Russia and Greece have a history of cordial relations and cultural ties, such as their shared Orthodox Christianity.
"Some would also argue that the new Greek government position is just a negotiating ploy in regard to its priority to renegotiate Greece's (bailout) program," Timothy Ash, head of emerging markets at Standard Bank, said in a note Wednesday.
"This might suggest that in exchange for concessions therein, the Greeks may ultimately fall into line with the consensus view within the EU over Ukraine."
He added that the weekend's Greek elections had added "yet another not insubstantial complication" to the crisis between Russia and Ukraine, and "my own discussion with Western government officials suggests they are fully aware of this."
Read MoreCan Europe resist Greek demands for a debt haircut?