Advances towards visa-free travel depend on the implementation of a number of "common steps" such as introducing biometric passports and preventing illegal migration.
"This decision has clear potential benefits to our citizens and for people-to-people contacts," said European Commission President José Manuel Barroso, who participated in EU-Russia summit. "But this will probably not happen next year."
Russia pledged to give at least €7.5 billion ($10 billion) to help indebted eurozone countries via the International Monetary Fund. Previous statements from Moscow had indicated $10 billion would be the upper limit.
The offer followed a summit of EU leaders last week, where nearly all countries agreed to a pact for tighter fiscal rules and to give new funds and loans to the IMF - with a provisional total of up to €200 billion.
"Russia has 41% of its currency reserves invested in euro or euro-nominated securities," President Dmitry Medvedev told the summit.
"Therefore we will provide aid ... and we are ready to invest," he said, adding Russia was also "ready to consider other support measures".
Medvedev visited Brussels against the background of declining economic fortunes on both sides and political controversy in Moscow.
Two weeks after parliamentary elections that drew accusations of fraud, Prime Minister Vladimir Putin confirmed yesterday he intends to appoint Medvedev as prime minister following a March election expected to return Putin to the presidency.
Herman Van Rompuy, president of the European Council, which represents EU member states' governments, criticised the elections - though tempered this by praising the handling of recent demonstrations and welcoming Russian government pledges to investigate problems with the elections.
"We are concerned by irregularities and lack of fairness," Van Rompuy told a news conference after meetings with Medvedev.
"And we are concerned by the detention of protestors. In contrast, the recent large demonstrations were peaceful and the authorities, in my view, handled it very well."
The EU and Russia have become heavily interdependent through energy and commercial links, but they also disagree sharply on some subjects.
Annual trade between the two sides is worth about €307 billion - about half the value of Russia's total foreign trade. Commercial links are expected to grow after Russia joins the World Trade Organisation, which is scheduled to be finalised in Geneva on Friday.
Visa-free travel could enhance economic and other links, officials say. Currently the 2.5 million or so Russians that visit the Schengen border-free area each year need to apply in advance for visas - which likely dissuades potential tourists to southern European countries such as Greece.
However, Russia has repeatedly criticised EU regulations, known as the third energy package, that seek to liberalise the European gas market by barring suppliers from controlling the transport infrastructure used to deliver their gas.
Medvedev has also said a proposed gas pipeline that would transport natural gas from Kazakhstan and Turkmenistan to Europe, circumventing both Russia and Iran, violated the interests of Caspian states and could damage the environment.
Still, Medvedev praised the launch last month of the first arm of the 1,224-kilometre Nord Stream pipeline from Western Siberia to Germany, which will initially handle 27.5 billion cubic metres of gas a year.
This is expected to rise to 55 billion cubic metres once a second adjacent pipeline is completed in 2012.
"In any case Russia remains a reliable exporter of hydrocarbons to Europe and this long term successful experience of joint work will be continued," he said.