The mass rally in Independence Square was a continuation of street protests that erupted in November following Mr Yanukovich's decision to abandon a free trade agreement with Europe in favour of closer cooperation with Russia.
The demonstration yesterday came a day after baton-wielding riot police tried to disperse protesters outside a Kiev courthouse, sparking clashes in which at least 10 people were injured.
Vitaly Klitschko, an opposition leader and former world heavyweight boxing champion, told the crowd that gathered yesterday waving national flags: "What are the next steps? We will fight protest peacefully.
"Today, the authorities use the militia as a weapon, silencing the people's mouths with batons."
Unless the vote is brought forward, a presidential race is not due until 2015.
Another opposition leader, Arseniy Yatsenyuk, called on the west to impose sanctions against senior state officials, including Interior Minister Vitaly Zakharchenko who, he said, had violated the constitution by authorising the use of force against protesters.