The European Union and Russia have both said Ukraine should have a "free choice" when it comes to choosing whether to pursue closer ties with the West or with Moscow.
Russian Foreign Minister Sergei Lavrov made the statement to journalists after he met in Brussels with the 28 EU foreign ministers.
"We discussed Ukraine and that it was our common agreement that everyone should respect the sovereignty of any country, including Ukraine and everyone should allow the people to make their free choice of how they want to develop their country and how they want to develop their state," Lavrov said.
At a separate press briefing after the talks, EU foreign-policy chief Catherine Ashton agreed that free choice was fundamental for every country but added, "it's very normal for countries to have agreements with many other countries."
Ashton also said signing a key political and trade deal with the EU would serve Ukraine's economic and political interests best.
"We believe that the [Association] Agreement provides the best way to address Ukraine's short-term economic challenges. [Ukraine's] signature too would send a powerful signal of confidence to international markets and to financial institutions," Ashton said. "And it also serves as a blueprint for political and economic reforms and therefore long term development perspectives."
Earlier in the day Ashton said financial concerns which Ukraine said prevented it from signing an Association Agreement with the bloc last month can be resolved.
The Kremlin, meanwhile, indicated it could offer financial and energy incentives to Ukrainian President Viktor Yanukovych when he visits Moscow on December 17.
Economic adviser Andrei Belousov said a loan to help Ukraine cope with its economic difficulties could be agreed between Yanukovych and Russian President Vladimir Putin.
Belousov did not say how much Russia would offer Ukraine. But sources in Ukraine said the deal could be worth $15 billion, with Moscow offering some $3 billion to $5 billion up front.
The most Brussels has so far offered Ukraine is 610 million euros ($838 million).
Ukrainian Energy Minister Eduard Stavytskyy said there was a great probability a deal could be reached on reducing the price of Russian gas for Ukraine.
Any agreement would signal a successful step taken by Moscow toward keeping Ukraine in its political and economic orbit.
Yanukovych last month made a U-turn and refused to sign an already-negotiated Association Agreement with the EU at a summit in Vilnius, apparently caving in to pressure from Russia, which wants Ukraine in its own customs union with Belarus and Kazakhstan.
WATCH: One participant of a rally for Yanukovych supporters on December 15 tells RFE/RL he has been paid $25 to rally for Yanukovych but in his heart he supports the pro-EU demonstrators in Independence Square.
Pro-EU demonstrations continued on December 16 in Kyiv, a day after a huge rally drew up to 200,000 people.
Protesters have planned another mass rally on December 17 to monitor Yanukovych's trip to Moscow.
Vitaly Klitschko, one of the leaders of the opposition, warned that Russian aid could come at a strategic price for Ukraine.
"We have information from different sources that there will be a cut in gas prices [for Ukraine] in exchange for a Ukrainian gas pipe. A gas transit system is a very important key strategic component of the economy, and we don't want Ukraine's interests to be given up," Klitschko said.
Arseniy Yatsenyuk, head of the Batkivshchyna (Fatherland) opposition party, has again urged Yanukovych to dismiss his govenment.
With reporting by Reuters, AP, AFP, and dpa