The EU’s foreign policy chief, Catherine Ashton is in Ukraine on Wednesday for more talks with the president and opposition leaders.
It comes as Viktor Yanukovych faces fresh demands from his rivals for a constitutional change that would seriously curtail his powers.
At least six people have been killed in the past two weeks in unprecedented politically-linked violence in Kyiv, whose centre is now a heavily-barricaded fortified protest zone.
But some do not feel the EU’s involvement will help bring a swift end to the crisis.
“As soon as the European Union gets involved Russia will get involved. It’s our business, and our country. We need to remove Yanukovych, and then to put in a new leader who will do all what we need,” said one demonstrator.
Fierce clashes between riot police and squads of radical protesters have prompted global concern that the ex-Soviet republic, a large buffer territory of 46 million people between Russia and the EU, might plunge into civil war.
Though there has been no violence in Kiev for several days, Western governments have warned Yanukovych that it risks flaring up again unless he can find a compromise with the opposition.