US Secretary of State John Kerry met with Ukrainian opposition leaders on Saturday on the sidelines of the conference and reaffirmed the US support for the opposition in Ukraine, Xinhua reported.
Kerry was reported to call on the opposition leaders to continue discussions with the Ukranian government. In an earlier speech made at the conference, Kerry said, "the US and Europe stand with people of Ukraine".
"Nowhere is the fight for a democratic, European future more important today than in Ukraine," Kerry said while addressing top diplomats and military officers here.
Anti-government protests and demonstrations that followed a decision of Ukraine to walk away from an association deal with the European Union (EU) last November, are still continuing in the country.
European Council President Herman Van Rompuy admitted that Ukraine is currently a common concern of European countries.
"Ukraine is on all our minds," he said. It is a sign that the EU has not given up its mind to woo Ukraine.
"The offer is still there," Van Rompuy said. "And we know time is on our side. The future of Ukraine belongs with the European Union."
The assertion made by Van Rompuy is perhaps not a common idea among people in Ukraine. At least Foreign Minister of Ukraine Leonid Kozhara, who was also present at the conference, has a different idea.
Kozhara said he was pro Europe, but stressed that Ukraine cannot quickly and simply make a decision in that regard. The "attractive" loan provided by Russia and reduction of natural gas prices as a result of a deal helped Ukraine stay afloat.
Kozhara blamed the opposition for not honouring a deal with the government, which, according to Kozhara, has met all the five demands put forward by the opposition.
Meanwhile, opposition leader Vitali Klychko accused the Ukrainian president for "terror and violence" in the country and insisted on the release of 300 protestors detained by police, the return of its constitution to the 2004 version and early presidential elections.
While West countries point fingers at Moscow for putting pressure on Kiev, which was allegedly part of the reason Ukraine refrain from signing the association deal, Russian diplomats lashed back at the West at the security conference.
Russian Foreign Minister Sergei Lavrov said the choice is being imposed on Ukraine and Russia is not going to be engaged in that.
"What does incitement of violent street protests have to do with the promotion of democracy? Why do we not hear condemnation of those who seize government buildings and attack police and use racist, anti-semitic and Nazi slogans?" he said.
Leonid Slutsky, chairman of the State Duma Committee on the Commonwealth of Independent States, Eurasian Integration and Compatriot Relationships, reaffirmed that Russia will continue to support Ukraine.
While some participants at the security conference voiced their concern about the situation, Kerry has been reported to call for a peaceful solution to the crisis.
Protests in Ukraine, which began last November to back the country's European integration, turned violent Jan 19, when radical activists attacked riot police with fireworks and petrol bombs.