The opposition demands that early parliamentary and presidential elections be held in Ukraine, leader of the UDAR opposition party Vitaliy Klitschko said.

"We demand that those, who were involved in beating students, be punished… That this disgraceful government headed by [Ukrainian Prime Minister Mykola] Azarov not exist. We demand complete reboot of the authorities. We need early presidential and parliamentary elections," Klitschko said when speaking on Kyiv's Independence Square, Maidan Nezalezhnosti, on Sunday.

Klitschko said he urged rally participants "to put the squeeze" peacefully on the incumbent authorities.

"Now we should express our view of the future: disrespect for the current authorities. And we call for a strike… I am certain that we can put the squeeze on the current authorities," Klitschko said.

Today's rally is an utterly peaceful one and any aggression will be considered to be a provocation, Klitschko said.

Opposition leaders have just given an ultimatum to Yanukovych, Klitschko said. They demand that political prisoners detained on Maidan be released, that those guilty of dispersing protesters and beating students be punished and that the government be dismissed.

Meanwhile leader of the Third Ukrainian Republic movement, former Ukrainian Interior Minister Yuriy Lutsenko said he urged Ukrainian President Viktor Yanukovych to sign the EU-Ukraine Association Agreement immediately and dismiss Azarov's government in order to resolve the political crisis in the country.

"You do not own all the power in Ukraine as it was on December 1. You have crossed the red line when our children were beaten and you deprived us of the prospect to become closer with the European Union. Now the only possible way out is signing the EU Association Agreement, now, immediately. And your Azarov's government is not a government already, it cannot rule anymore the country sacked by your satellites," Lutsenko said when speaking at the rally.

Yanukovych should realize that after December 1 he cannot consider himself to be "the sovereign of Ukraine" anymore, Lutsenko said.

"We have gathered in order to say that we deny trust to you" – Viktor Yanukovych, Mykola Azarov and the entire gang, Lutsenko said.