MEPs have asked EU governments to prepare sanctions against members of the Ukrainian government.
The non-binding motion calls for travels bans, as well as the freezing of assets.
Commission officials have stressed the need for political dialogue, but parliamentarians say time is running out to deal with the crisis.
Elmar Brok, German MEP said:
“People who are personally responsible for violence, for putting people in jail (and) torture, people who make such laws supporting it, might lose the right for entry into the EU.”
There has been talk that the EU might make a new offer of financial aid to Kyiv.
Marek Siwiec, Polish Mep said:
“Money is like fuel. But (in) sending the fuel, you have to be sure that the machine is service effective.”
One centre-right Polish MEP said constitutional reform and respect for human rights was essential if Ukraine ever wanted closer ties with Brussels.
“The constitution that is applied now is illegitimate, because it was changed by the supreme court and not by the parliament. It created competences of a presidential republic for which President Yanukovych was not at all elected.”
EU foreign policy chief Catherine Ashton was in the Ukrainian capital on Wednesday for talks with the Ukrainian president.