Thousands of protesters attacked the ruling-party headquarters and tried to march on parliament, reports said.
Tumultuous scenes have also been reported inside parliament, where opposition MPs are pushing for a vote on replacing the constitution.
The move is aimed at curbing President Viktor Yanukovych's powers.
The opposition had repeatedly warned that failure to act would further inflame mass anti-government protests - and these have reignited after a period of relative calm.
Ukraine's unrest began in November, when Mr Yanukovych backed away from an association and free trade deal with the European Union, and instead agreed to a large loan from Russia.
Moscow wants Ukraine to join the Russia-led customs union, which also has Belarus and Kazakhstan as 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 Yanukovych's party, temporarily smashing their way in before being forced out by police, reported 5 Kanal TV.
Several people are reported to have been injured, including three interior ministry troops and a news photographer.
Inside parliament, opposition leader Vitaly Klitschko appealed to Mr Yanukovych to take the riot police off the streets to avert further "conflict in society".
Earlier, opposition MPs blocked the parliamentary rostrum in protest after parliamentary staff refused to register their resolution on reinstating the 2004 constitution.
"Our deputies have just returned from the draft law registration section," opposition leader Arseniy Yatsenyuk said, according to Interfax-Ukraine news agency.
"They have just simply locked the doors there on the instructions of [Speaker Volodymyr] Rybak and are refusing even to talk to Ukrainian people's deputies, let alone register the resolution."
Mr Rybak is a member of Mr Yanukovych's ruling Party of Regions.
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. MPs who support the president have argued that different proposals on how to return to the previous constitution legitimately have not been thoroughly discussed, and more time is needed to iron out all the differences between the two sides.
In a separate development, Russian Finance Minister Anton Siluanov said Moscow would provide Ukraine with a new $2bn (£1.2bn) tranche of loans "this week".
In December, Moscow pledged $15bn to back Ukraine's struggling economy, but so far only $3bn has been transferred.
The Kremlin had hinted it would freeze the loan until a new government acceptable to Moscow was formed after Ukrainian PM Mykola Azarov resigned last month.
On Monday, an amnesty for anti-government protesters in Ukraine came into force after demonstrators ended their occupation of government buildings in Kiev and in the regions.
Protesters had held some of the buildings for more than two months.
But a sprawling tent city remains in Kiev's central square, where some denounced the decision to end the occupations.
- Opposition's draft proposal in essence calls for a return to 2004 constitution that shifted key powers from president to parliament 2004 constitution repealed in 2010, shortly after President Yanukovych came to power.
- Reforms would see president stripped of powers to appoint PM, cabinet members and regional governors - and possibly snap elections.
- Ruling party is reportedly amenable to the proposal in theory, but says it needs to be discussed by non-governmental organisations and sent to Council of Europe's Venice Commission for Review.