Late last month, Ukraine and the EU signed a long-delayed Association Agreement -- the very deal whose last-minute refusal last year by then president Viktor Yanukovych plunged the country into chaos.
The agreement opens up Ukraine to EU imports. Moscow worries this will also allow cheap European products to flood into Russia, which has its own free-trade deal with Kiev.
EU Trade Commissioner Karel De Gucht said the parties agreed to address Russia's concerns at a high level over the coming weeks, with a new ministerial meeting set for September 12.
After the meeting, Ulyukayev said the association deal carried "dangers for the Russian economy," but that the parties had agreed on a framework for more talks.
More From This Section
Moscow has announced trade measures against Kiev, including a ban on dairy imports, since the EU deal was signed amid ongoing battles between Ukrainian government forces and pro-Russian separatists in the restive east.
Brussels has also brokered talks over a bitter gas-price dispute between Kiev and Moscow that has threatened to stop the flow of energy from Russia to the EU.