But Jean-Claude Juncker insisted there will be no letup of sanctions.
"We will not see a weakening of European positions," Juncker told reporters. "We will extend the sanctions against Russia and we will make it clear that we don't agree with the actions of Russia in Ukraine and Crimea in any way."
Russia too is downplaying the prospects of a more meaningful diplomatic thaw.
Like the US, the 28-nation EU has effectively frozen ties with Russia and imposed sanctions after its 2014 seizure of the Crimean Peninsula.
Juncker stressed he would be addressing a Russian economic conference in St Petersburg in mid-June and indicated he would likely meet with Russian President Vladimir Putin, who is scheduled to attend the meeting.
"I will speak to those who are there," Juncker said. "I find it important that at least in economic questions we try to get closer together."
Russia's sanctions-struck economy contracted by nearly 4 percent last year while Russia's retaliatory boycott of EU food products has spurred inflation.
But Peskov stopped short of calling this a sign that EU-Russia ties were on the mend.
"I would not be too optimistic and spot the signs of a breakthrough anywhere," Peskov said. Mutual sanctions and loss of trust would be "impossible to get rid of overnight.
