Police Monday also took up positions outside the perimeter of the main protest sites as demonstrators used benches, planks and other goods to fortify the blockade that has closed of the area for about a week, the New York Times reported.
The Times said some demonstrators appeared to be evacuating the occupied Kiev City Hall, anticipating that it would be a target of any enforcement action.
At Independence Square, several thousand people milled about the day after a huge rally saw a statue of Russian communist revolutionary Vladimir Lenin toppled and smashed with hammers.
Protesters are angered at Yanukovych's decision not to sign sweeping political and trade agreements with the European Union. After indicating he would sign the accords, Yanukovych did a U-turn, saying instead he would pursue building relations with Russia.
International concern over the unrest deepened Sunday, as U.N. Secretary-General Ban Ki-moon telephoned Yanukovych and Western leaders called on him to respond to the demonstrators' demands.
The Times said the devolving disorder touched off talk that Yanukovych would declare a state of emergency and rely on force in the removal of demonstrators who have occupied Independence Square and several public buildings.
Ukrainian government had officials promised Western diplomats they would not oust peaceful protesters by force, after police faced heavy criticism for its handling of clashes Nov. 30 in which hundreds of people were injured.
Reports also surfaced Sunday that charges of treason were being prepared against three opposition leaders in Parliament who have been at the forefront of the demonstrations, the times said.
Arseniy P. Yatsenyuk, of the opposition Fatherland party, called for civil disobedience if Yanukovych tried to impose martial law.
"In the case that a state of emergency is declared, everyone should go to [Independence Square]," Yatsenyuk said.