Russian President Dmitry Medvedev is playing host to top EU officials for talks in the southern city of Rostov-on-Don. The European Union is Russia's No. 1 trading partner, and EU nations account for 80 percent of all investment in Russia.
Deputy Foreign Minister Alexander Grushko urged European leaders to show political will and scrap entry visas for Russians.
"We would like to see our European partners formulate their vision of this issue at the Russia-EU summit," he said at a Friday briefing.
"It's time to make political decisions."
Russia has been seeking visa-free travel to Europe for years, but EU nations point to the violence in Russia's volatile North Caucasus region and the nation's porous borders with its ex-Soviet neighbors as reasons for the border controls.
Grushko argues that Russia has met European demands, particularly by signing agreements with EU nations on repatriation of illegal migrants.
Unlike a few years ago, Russia is anxious to attract foreign investments and seeks closer cooperation and more transparent borders with the EU. As the global downturn weighed down on oil and gas prices, Russia, a leading energy exporter, has shown a stronger interest in modernizing its economy.
Russia and the EU are working on a partnership that would help Russia gain easier access to Western technology, something Prime Minister Vladimir Putin has recently described as a "turning point" in the bilateral relations.
In return, Europe expects Russia to crack down on corruption, strengthen the rule of law and conduct other reforms.
It is not clear, however, whether Russian leaders are poised for such profound changes.
"What Russia needs and wants most clearly is the economic support that would allow the current system of political and economic management to keep going and eventually make it through this crisis," said Sam Greene, a political analyst at the Carnegie Moscow Center.
Europe can provide that, but it still has to understand what it stands to gain, he added.
"Neither side has a good understanding of what the other side wants from their relationship," Greene said.
The summit opens as Europe is struggling with a government debt crisis that is quickly spreading across the continent.
EU nations' troubles at home are likely to make foreign policy coordination even more challenging than before, and key issues such as Russia's attempts to take control over Ukraine's gas pipeline network might not get as much attention at the summit as they deserve.