One of them, former boxer Vitali Klitschko, has said he will lead pro-EU protesters "on the attack" if snap elections are not called.
Mr Yanukovych has asked the speaker of parliament to hold an emergency session next week to discuss the crisis.
Two activists were killed in clashes with police in Kiev on Wednesday.
Prosecutors confirmed they had died from gunshot wounds. They were the first fatalities since the anti-government protests flared up in late November over Mr Yanukovych's decision to pull out of a landmark treaty with the EU.