Protesters attacked the ruling-party headquarters and tried to march on parliament, reports said.
Tumultuous scenes have also been reported inside parliament where opposition lawmakers are pushing for a vote on replacing the constitution.
The move is aimed at curbing President Viktor Yanukovych’s powers.
The opposition has repeatedly warned that failure to act will further inflame mass anti-government protests.
Ukraine’s unrest began in November, when Viktor Yanukovych backed away from an association and free trade deal with the European Union, and instead agreed to a loan from Russia.
Moscow wants Ukraine to join the Russia-led customs union, where Belarus and Kazakhstan are also members.
Both the EU and Russia have accused each other of interfering in Ukraine’s affairs.
Tens of thousands of protesters trying to march on the parliament building have been blocked by lines of police vehicles, according to reports from Kiev.
Some are ripping up cobblestones to throw at police, and others are throwing smoke bombs, while police are responding with stun and smoke grenades and rubber bullets.
Protesters also attacked the headquarters of President Viktor Yanukovych’s ruling party.
Several people have been injured, both protesters and police officers, local media reported.
Inside parliament, reported Interfax-Ukraine news agency, about 50 opposition lawmakers blocked the parliamentary rostrum in protest after parliamentary staff refused to register their resolution on reinstating the 2004 constitution.
The opposition has been pushing for weeks for a return to the 2004 constitution, which would mean President Yanukovych losing some of the powers he has gained since his election in 2010.
The changes would mean that parliament – not the president – would appoint the prime minister and most cabinet members, as well as regional governors.
The move could also lead to snap presidential elections – a key demand of the opposition.
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