"We will not step back until we are heard," Klitschko was quoted as saying Sunday.
Russian news agency RIA Novosti reported thousands of demonstrators turned out in downtown Kiev during the weekend to express frustration with the Ukrainian government.
A government decision in November to suspend efforts to sign free-trade and association agreements with the European Union sparked nationwide protests.
The government of the former Soviet republic said the decision was made to protect its economic ties to Russia, and that it wasn't abandoning the EU agreements completely.
In a New Year's Day message, Ukrainian President Viktor Yanukovych said collective will was needed to weather the political storm.
"This path is extremely challenging, but we must go through it jointly, side by side," he said.