added, "The U.S. will continue to consider additional steps - including sanctions - in response to the use of violence."
The rally, the biggest of the new year, was the latest in a cycle of public protests in the former Soviet republic since Yanukovich made a policy U-turn in November away from the European Union towards Russia, Ukraine's former Soviet overlord.
Several big protests in December attracted hundreds of thousands of people, while thousands maintained a vigil in a Kiev square demanding Yanukovich resign. Since the new year demonstrations have become smaller, but hundreds of people are still camping in the square and 50,000 turned out a week ago.
The court ban on protests published on Wednesday, and last Thursday's legislation aimed at prohibiting all form of public protests, have inflamed tensions again.
The laws ban any unauthorised installation of tents, stages or use of loudspeakers in public.
Heavy jail sentences were imposed for participation in "mass disorder" and the wearing of face-masks or protective helmets. Dissemination of "extremist" or libellous information about the country's leaders was outlawed.
In a gesture of scorn for the helmet ban, many protesters on Sunday wore saucepans and colanders on their heads.
The crisis has highlighted a divide in the country of 46 million people between those, particularly in Russian-speaking eastern areas, who identify more closely with a shared past with Russia, and those, especially in the Ukrainian-speaking parts of western and central Ukraine, who look westwards.
Opposition leaders announced an action plan to gather people's signatures expressing no confidence in the leadership of Yanukovich and parliament.
Denouncing as unconstitutional last Thursday's hurried vote in parliament by Yanukovich loyalists, they called for moves to set up a parallel structure of power - including a people's assembly and a new constitution.
"Yanukovich and his henchmen want to steal our country. Ukraine is united as never before in its struggle against those in power today, in its determination not to allow a dictatorship," Klitschko, the strongest potential challenger for the presidency, told the crowds on Independence Square.
CALLS FOR RESTRAINT
Opposition leaders were at