Supporters and opponents of Ukrainian President Viktor Yanukovich scuffled as both sides held large rallies in the capital Kiev on Saturday, police and local media said.

A dozen young men hurled stones and plastic water bottles at opposition supporters and were then pushed away by police in riot gear, television footage showed.

Anti-Yanukovich protesters also fought back and at one point some of them tried to drag the crew from a military vehicle that carried messages mocking opposition leaders, pictures showed.

"Several people have been injured," police said in a statement, adding that they had intervened to end the fight which happened a block away from the main opposition rally.

Pro-Western Batkivshchyna (Fatherland), liberal UDAR (Punch) and far-right Svoboda have been holding rallies across Ukraine, accusing Yanukovich of failing to pursue his declared goal of European integration, and demanding the release of jailed Batkivshchyna leader, former Prime Minister Yulia Tymoshenko.

Tymoshenko, a leader of the 2004 Orange Revolution protests that derailed Yanukovich's first bid for the presidency, was sentenced to seven years in prison in 2011 on charges of abuse of office in a case the West has called politically motivated.

The European Union has indicated that Tymoshenko's continued imprisonment would make it impossible to sign landmark association and free trade deals with Ukraine tentatively planned for November.

Yanukovich's Party of the Regions, in turn, held its own rally nearby to condemn what it called the rise of "neo-fascism" in Ukraine, a stab at the far-right Svoboda party and its opposition allies.

Allied in Europe with France's National Front, the British National Party and Hungary's Jobbik among others, Svoboda was previously known as the Social-National Party, an echo of the National Socialist, or Nazi Party.

Nowadays, however, the party denies being anti-Semitic or sympathetic to Nazism.

At the opposition rally on Saturday, Svoboda, Batkivshchyna and UDAR said they would work together to defeat Yanukovich in the 2015 presidential election when he is widely expected to seek a second term.