Speaking to CNBC in Kiev, United Nations Deputy Secretary General Jan Eliasson conceded that events in Crimea could be the prelude to a new "Cold War" between the West and Russia. He said it was a risk he "wouldn't accept" however.
"I think basically all people realize that de-escalation is the right way to go," Eliasson said. "If this crisis enters the mode of military... we all lose and I think everybody realizes that. Feelings are running high, understandably, but it is important now that cool heads prevail."
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Ukraine pulled out of a trade deal with the EU under Russian pressure last year, sparking months of protests in Kiev and the February 22 ouster of President Viktor Yanukovich, a Russian ally.
Ukraine says Russia has occupied Crimea, where its Black Sea fleet is based, provoking an international outcry and sharp falls in financial markets on Monday, though they have since stabilized.
The foreign ministers of Russia, the United States, Britain, and Germany met their French counterpart and French President Francois Hollande in Paris to try to start a diplomatic process to defuse the crisis.
But diplomats said it was not clear whether Russian Foreign Minister Sergei Lavrov would take the crucial step of attending talks with Ukraine's new foreign minister, a member of a government Moscow has described as illegitimate.
U.S. Secretary of State John Kerry left the meeting at Hollande's office without making any statement.
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Earlier, Lavrov repeated Moscow's assertion - ridiculed by the West - that the troops that have seized control of the Black Sea peninsula are not under Russian command.
Asked whether Moscow would order forces in Crimea back to their bases, Lavrov told a questioner in Madrid: "If you mean the self-defense units created by the inhabitants of Crimea, we give them no orders, they take no orders from us.
"As for the military personnel of the Black Sea Fleet, they are in their deployment sites. Yes, additional vigilance measures were taken to safeguard the sites ... We will do everything not to allow any bloodshed."
Russia did not attend a meeting with Kerry, British Foreign Secretary William Hague and Ukrainian Foreign Minister Andriy Deshchytsia of the so-called Budapest group created to assure Ukraine's security after it abandoned nuclear weapons in 1994.
But Kerry and Hague said they would try to bring the Russian and Ukrainian ministers together later in the day.
Poland's foreign minister tweeted that he would attend a meeting in Paris with those two ministers plus the United States, Germany, Britain, France and the Organisation for Security and Cooperation in Europe (OSCE).
But there was no confirmation that all sides would attend the session, which could be the first step in a diplomatic mediation process.
Lavrov was later due to hold the first face-to-face talks with his U.S. counterpart since the crisis escalated, on the sidelines of a conference on Lebanon attended by the five permanent members of the U.N. Security Council.
NATO and Russia were also set to hold talks in Brussels amid concerns that a standoff between Russian and Ukrainian forces in Crimea could still spark violence, or that Moscow could also intervene in Russian-speaking eastern Ukraine.
In a sign of heightened tensions in the east, a pro-Russian crowd in Donetsk, Yanukovich's hometown, recaptured a regional administration building they had occupied before being ejected by police, a Reuters witness said.
The West is pushing for Russia to return troops to barracks, accept international monitors in Crimea and Ukraine and negotiate a solution to the crisis through a "contact group" probably under the auspices of a pan-European security body.
France said European Union leaders meeting in Brussels on Thursday could decide on sanctions against Russia if there is no "de-escalation" by then. Other EU countries, including Germany, are more reticent about sanctions.
French Foreign Minister Laurent Fabius said early measures could include restrictions on visas, the assets of individuals and existing discussions on economic ties with Russia.
President Vladimir Putin on Tuesday defended Russia's actions in Crimea, which used to be Russian territory, and said he would use force only as a last resort.