"Let's be wiser [and] quietly settle [differences] with each other on our native land," he was quoted by the National News Agency of Ukraine as saying. "We have enough experience to overcome any crisis."
Ukraine was criticized by Western governments after police were accused of using force against demonstrators in Kiev.
The British government Friday warned of the possibility for further unrest during the weekend.
"Protests and demonstrations are occurring in Kyiv [Kiev] and many other cities," the warning read. "Some of these have resulted in scuffles between demonstrators and the police."
A Ukrainian decision in November to suspend efforts to sign free trade and association agreements with the European Union sparked widespread protests in the country. The Yanukovych government said the decision was made to protect economic ties to Russia, though the president has since given the EU assurances he was still interested in the agreement.
EU Neighborhood Policy Commissioner Stefan Fule said from Brussels he was urging Kiev to sign the deal as soon as possible.
"There is also no better signal to send to the citizens who continue to demonstrate peacefully for a secure and prosperous future for them and their children, than a rapid signature," he said in a statement.